X-1 For the function f(x)= find f"(x), the third derivative of f, and f)(x), the fourth derivative of X-3' f"(x) =

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: 3x y=3- + Arccos V8-x3

A: We have to find out the first derivative  .

Q: 6. Determine the 19th derivative of the function y=sin(x). Fully explain the process you used to…

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Q: e first derivative for the +1)(x +2) 2)

A: Find the first derivative. y=(x+1)(x+2)(x-1)(x-2)

Q: second derivative of  y=x(x-4)3

A: Given function is y = x(x – 4)^3. Differentiate with respect to x on both sides.

Q: Compute the derivative of the function y = 7 sin¬'(x) at the point x = (Use symbolic notation and…

A: A detailed solution is given below

Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: Find the derivative of y=x^(7sinx). (x>0).

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Q: Find the derivative of the function. f(x) = ln(6x) f '(x) =

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Q: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

A: Given function: y=x-12x-x2-arccosx-1

Q: 4. Find the derivative of the function using the definition of derivative. State the domain of the…

A: f'(x) = limh→0 f(x+h)-f(x)h. The domain of the function is the set of all possible input values for…

Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent…

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Q: how do you find the second derivative of f(x)=ln(x)?

A: on differentiation we get

Q: Find the derivative if f(x)= ((x/2) + (x √x))ex

A: The given function is fx=x2+xxex. Obtain the derivative as follows.

Q: the derivative of the function f (x) = arccos (1 / x)

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Q: using the definition of derivative to find f'(x) for the function:f(x)=4/x. How do I solve this?

A: Given problem is to find the derivative of f(x) = 4/x

Q: Find the derivative of the function.   f(x) = ln(x + 4)   f'(x)=

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Q: Using the derivative of 10x determine the value of the derivative at   x=3 and x=5

A: Derivative ( xn) = n xn-1

Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: Find an equation of the tangent line at the given point.  f(x)=3/x2  , at x= -1

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Q: Find the derivative of y with respect to x Y=5 ln (3 ln x)

A: Given, y=5 ln (3 ln x) We have to find derivative of y with respect to x.

Q: Derivative of y with respect to x

A: taking logrithum both sides and solve the question.

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: Find the derivative of the function. f(x) = ln(x2 + 1)2

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Q: Find the derivative of the function. f(x) = ln(2 − x2)   Thank you for your help!

A: Given function f(x) = ln(2-x2). Here we need to find the derivative of f(x) with respect to x.We use…

Q: Find the derivative of: y=x^(7sin(x)). (x>0).

A: Multiplication rule of derivative is used.

Q: Find the derivative of the algebraic functions f(x) = x (1-) x+3, : g(x) = x + cotx

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Q: Find the derivative of the function. y = square root of 1 - x2 − x cos−1(x)

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Q: Compute the derivative of the function y = 6 cos- (4x) at the point x = (Use symbolic notation and…

A: Solution ) y = 6 cos-14x Differentiate with respect to x  y' = 6 d/dx (cos-14x) [ we know that  d/dx…

Q: Find the derivative of a function at a given point F(x)= 2e^x-x at x=1 F(x)= x^3-5x at x=2

A: We have to find derivatives of the function: Fx=2ex-x at x=1 and Fx=x3-5x at x=2. We know the…

Q: Find the derivative of f(x) = ln(2x^3 + x).

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Q: Find the first derivative of y=3x^2-2√x

A: We have to find the derivative from the given function

Q: Find the derivative of these functions with respect to x.   xsin-1(In(x))

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Q: Find the equation of the tangent line to the curve given by f(x) = x2 ln x at the point  (1, 0)

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Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: 31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not…

A: Given: fx=x2+x     , x≤13x-2   ,  x>1

Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

Q: derivative

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Q: Find the instantaneous rate of change of f(x) = x* at x = 3. %3D Find the derivative of g(x) = x + x…

A: 1) Given, f(x)=x2 at x=3 Use the definition of instantaneous rate of change: The instantaneous rate…

Q: Find all x-values where g(x) = −(x^3 )+ 3(x^2 )+ 9x − 20 has a horizontal tangent line (that is,…

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Q: Use the fact that the derivative of the function f(x) =- is f'(x) = to find the equation of the…

A: We need to find the equation of tangent to the graph of f(x).

Q: 10.(a) Find the derivative of the function f(x) =x² +2 using the definition of derivative. (b) What…

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Q: Find the derivative of the function. f(x) = (2x2 − x)ln x   f'(x)=

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Q: Find the derivative of the function. f(x) = ln(4 − x6) f '(x) =

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Q: Given f(x)=x(x-1). a) Find first derivatives of function f(x) using product rule and chain rule.

A: Our objective is to find the derivative and critical points.