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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 critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A: Given that the function is        f(x) = x e-x^2

Q: Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics…

A: Given query is to find the time when concentration is maximum and rate of change nis increasing.

Q: Find the first derivative of the function y = 2ArcsinV(x/2) %3D

A: Consider the given function, y=2Arcsinx2 It also can be written as, y=2Arcsinx2=2sin-1x2

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: f (x) = sec t dt %3D

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Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A: To find the antiderivative we integrate the given function c=integration constant

Q: Differentiate the function. y = etan(θ)

A: Given y=etanθ Use chain rule of differentiation to differentiate the given function.

Q: Sarah is asked to find the maximum value of a function. Not having a complete understanding of the…

A: If we want to find the maximum or minimum values of a function then follows the steps mentioned…

Q: Find the derivative of the function at the given number. f(x) = 3 – 4x + x², at -1 %3D f'(-1) = %3D

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Q: Determine the second derivative of f (x)= x 'e* at x = -2 with a step-size of h=0.50 using Central…

A: We have to find the second derivative of the following function at x=-2 with step size h=0.5 using…

Q: pret 30. f(x)= e2! dt 2-x

A: Given that: f(x)=∫2-xxexe2tdx

Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

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Q: . Find the equation of a line tangent to the graph of f (x) = cotx at x = T/4. .Find the derivative…

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Q: Find the first derivative of f(x) = e3r

A: To find the first derivative of fx=x3e3x. Solution: Quotient rule of derivative states that:…

Q: Find the derivative of the function. f(0= cosh? (2t2 + 9) a. st sinh (2t² + 9) b. st cosh (2t² + 9)…

A: Given  ft=cosh22t2+9 The chain rule is used in differentiating the above function F'x=f'gxg'x

Q: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: y=C1x + C2e + x2

A: The givne equation is:y=C1x+C2e-x+x2To eliminate the arbitrary constant/s

Q: y у %3 4a/сosh a

A: Consider the given hyperbolic function y=4acosha The given function can be written as, y=4acosha=4a…

Q: 54th Dorivative: fle)=2-4sin (a2)

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Q: find the first derivative f'(x) at the point x 1.3. Use two point central difference

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Q: Compute the derivative of the function f(x) = 5x² + 3x at the point x = 4. %3D (Give your answer as…

A: We have to find the derivative at that point

Q: ABANATUAN CITY B. Compute the derivative function f using the definition of the derivative. Show…

A: Using definition of derivatives.

Q: A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides…

A: Explanation of the answer is as follows

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Find the derivative of the function. y = 9 arcsin) – x/9 – x² Step 1 Rewrite the given function y =…

A: Given: --------------------------------------------------------------------------------------------…

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

A: The slope of tangent to a curve y=fx  at point a,b is given by dydxx=a.

Q: (5) Match the graphs of the functions to the graphs of their second derivatives. Original Functions…

A: Given: a function their derivative.

Q: How to solve this please? Estimate the first derivative of f(x)=2ln(1+x) using two-point forward…

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Q: f'(x) = (2x – 1)ee".

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Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx *please explain step by…

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Q: Use the first and second derivative to graph the following function. Label all critical points,…

A: Given that: y=4x3-4x2-8x

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: – x* – 6x2 + 5x + 12 , use either the First Derivative Test OR the Given the function f(x) = Second…

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Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: Q4/ Explain the rule of maximum and minimum using Derivatives with an еxample?

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Q: b) Use second derivative test to find absolute maximum and minimum values of f (x, у) 3 Зху — 6х —…

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Q: Determine the second derivative of f (x)=x²e* at x =-2 with a step-size of h=0.50 using Central…

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Q: Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3…

A: We have to find derivative of Given function.

Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.) y=…

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Q: The first derivative of a continuous function y = f(x) is y' = x(x- 21). Find y" and then use the…

A: Given: i. The first derivative of a continuous function y=fx.ii. y'=xx-212 To Find: i. y''ii. Use…

Q: Find the derivative of y = arctan(x² + 3)

A: To find: The derivative of y=tan-1x2+3. Formula used: Chain rule of derivative: fgx'=f'gx·g'x Power…

Q: Find the first derivative by increment method. Show your complete solution V7x – 12 Upload your…

A: The given function is 7x-12

Q: Find the derivative of the function. show all work y=(x-10)(x^2+2x) all over x^3

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Q: X-2 %3D

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Q: Find the first derivative by increment method. Show your complete solution. V12x – 3 Irolim Exam…

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Q: Find the derivative of the function. Simplify wherepossible  x lnarctan x

A: Let f(x)=xlnarctanxDerivative formula:ddxlnx=1xddxtan-1x=11+x2arctanx=tan-1x