Q: Find the derivative of the function. Simplify where possible. f(x) = x In(arctan x)
A: Given: The above function contains two functions, so the product rule is used to differentiate.
Q: Find the derivative of the function by the limit process. f(x)= 2/x2
A:
Q: Find the derivative of f(x) = tan tan (3x2+2x)( Ans: (6x + 2) sec2 (3x2+2x) solution?
A: Let,
Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)
A: We use the limit definition of the derivative
Q: calculate the derivative with respect to x. ln(x2 + y2) = x + 4
A: Given function lnx2+y2=x+4 Differentiate the above function w.r.t 'x' ddxlnx2+y2=ddxx+4…
Q: Find the derivative of ƒ (x) = 5ª In (x).
A:
Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…
A:
Q: Find the derivative of f(x) = 1 at x = 3
A: The given function is: fx=1x Using the formula of derivative i.e., ddxxn=nxn-1
Q: Find the derivative of the function y = arctan x + x 1+x²
A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2 ..........1ddxuv=vdudx-udvdxv2…
Q: Find the derivative of the function f(x) = tanh(4x2 + 3x)
A:
Q: show that nth derivative of f(x)=x^2/(2x+1)(2x+3)
A: nth derivative of f(x)=x2(2x+1)(2x+3) f(x) can be written as by using synthetic division method…
Q: Find the derivative of f(x) = 2(x² + 3x) cos(sin(x³)).
A: I have used product re and derived of composition of two function
Q: 13. f(x) = e* In x
A:
Q: Find the derivative of the function. h(x) = x2 arctan(5x)
A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x
Q: Find the derivative of f(x) = Inx + 1].
A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]
Q: Estimate the derivative of f(x) = sin x at x = π/6.
A: Given, f(x) = sin x at x=π6
Q: compute the derivative. f (x) = ln(ex − 4x)
A: We can use chain rule ( Nested function form ) of differentiation to find the derivative. According…
Q: Find the derivative of the function. rlx) = [in[x*}}°
A:
Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |
A: Given : To find the derivative of the given function f(x) = x3 -…
Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…
A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…
Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.
A:
Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =
A: h(x)=x2tan-1(x)
Q: Find the derivative of f(x)= xtan(x)
A:
Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ
A: Explanation of the answer is as follows
Q: 3. Find the derivative of f (x) tan (5x + 7), by first principle of differentiation
A: Given function is By first principle of differentiation, we have
Q: 3/x +1 f(x) = X+2 at x = -1
A:
Q: Find the derivative of the function y= arctan x +x/1+x2
A:
Q: Find the derivative of f(x)= (x^2)sinx
A:
Q: Find the derivative of y=ln [tan-1(7x5)] with respect to x.
A:
Q: Find the derivative of the function by the limit process. f(x) = 1/x2
A: Here the given function The first derivative of function f(x) is defined by limit prosses as
Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2
A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…
Q: Find the derivative of the function. y = tan−1 (square root of x - 4)
A: Consider the given function. y=tan-1x-4 The objective of the problem is to find the derivative of…
Q: Can you help me step by step?
A: To differentiate the given expression y=f(x)
Q: Find the derivative of the function by the limit process. f(x) = vX +7
A: Given, The function is fx=x+7.
Q: Find the derivative of the function h(x) = x2 arctan5x
A: The given function is h(x) = x2 arctan5x
Q: What is the derivative of f(x)=2sin(x) at the point x=−π/2?
A: To find the derivative of fx=2 sinx, at the point x=-π2.
Q: Find the derivative of the function
A: We have to find the derivatives of the function: y=x tan-12x-14ln1+4x2 If two functions are in…
Q: Solve for the derivative of the function using chain rule. 7. f(x)= sin(e3x)
A:
Q: ,2, (x²–1)* Dx (1+8x)5
A: To Determine: find the derivative using chain rule Given: we have y=x2-141+8x5 Explanation: we have…
Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)
A:
Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.
A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…
Q: f(x) = 3 sin 1 (x²)
A:
Q: Find the derivative of f ( x ) = 6 sin ^2 ( x ) + 6 cos^2 ( x ) at x = -6.5
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Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)
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Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.
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Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)
A:
Q: Find the derivative of the function y using the increment method or three- step rule. vx +1
A:
Q: Find the derivative of y = arccos x + x 1-x²
A:
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- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x)=6*e-x , a=−0.1 Set the center of the linearization as x=0 The linearization is L(x)equals=_______________
- A differentiable function has the value y(-1)=1 and the derivative value y’(-1)=2 approximate the value of y(-1.1)Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.) g(x) = 20(1+ 1/x + 1/x2 ), [−5, 5] Step 1: Begin by finding the derivative of g(x). Step 2: Find the critical numbers and points of discontinuity. (Enter your answers as a comma-separated list.) x = Step 4: Find the absolute extrema. (If an answer does not exist, enter DNE.) absolute maximum (x, y) = absolute minimum (x, y) =My topic is about Higher Order Derivatives and Optimization for reference. A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 10 in by 17 in by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the cut-off square so that the box has the largest possible volume.
- Hi, one more question. I am defining the max and mix value of a function, and I use the Lagrange method - I would need help forming the function pair in this kind of question (aka forming partial derivative for x1 and x2). Could you help with this? The function is f(x1,x2)=x1x2 and the condition is the latter function seen in the picture.Find relative extrema of the function. Use the second derivative test when applicable. (If an answer does not exist, enter DNE). 1. f(x) = 15x^2 - x^3 Relative Maximum = ? Relative Minimum = ? 2. f(x) = x^4 + 4x^3 -1 Relative Maximum = ? Relative Minimum = ?Finding a second derivative. Find d^2y/dx^2 implicity in terms of x and y
- 4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3.A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer.B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning.C. Find the value of f(-1).2-22 Differentiate the function: f(x) = log10(√x ) ? Please show work along with the rule used for derivatives of logs - Thank you!A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides. State the formula for the volume of a rectangular prism (aka box). Express the volume formula as a function of x. What is the domain of V? Find the derivative of V(x) with respect to x. Find the function values at the critical number/s and at the endpoints. What is the largest possible volume of the box? What is the length of the side of the cut-out square that will make the box which has the largest possible volume?