Find the derivative of the following function F(x) = / e (2t – 1)³ dt x5 using the Fundamental Theorem of Calculus. F'(x) = %3D 2.

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Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

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Q: Calculate the derivative d In (t)dt dx 5 using Part 2 of the Fundamental Theorem of Calculus.…

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Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: Find the partial derivative of the given In[y? sec(x²y²)].

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Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

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Q: Use partial differentiation to find the derivative of the implicit function dy (3x'y-1)+ 7xy = 9…

A: We will use the given formula to solve this question.

Q: In (3x) Find the derivative of y with respect to x if y= sin (7 e') dt. dy dx

A: Given : A function is given as: y=∫0ln3xsin7etdt To find : The derivative of the function y.…

Q: Find the derivative of y with respect to x. y = 8 In (4 In x) dy dx II

A: Topic:- derivatives

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

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Q: Find the differential d8y of the function y=exsinx.

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Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: Find the derivative of the function. %3D y = log |3- 5x| dy

A: Here , we will differentiate y  with respect to X  .

Q: Use the Fundamental Theorem of Calculus to find the derivative of y- " cos t dt t12

A: Given that  y=∫-9xcos tt12dt

Q: Find the derivative of F(x) = 4 sin(t) dt. 3x %3D dx cos(x)

A: Solve the following

Q: Find the derivative of the given function. 5x y= In 6+x dy dx

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Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Find the derivative of the function

A: Given function, Fx=∫πlnxcoset dt

Q: Find the derivative of the function y = In(3t + 4). %3D dy dt

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Q: (3) Compute the derivative of the function e2t cos tdt.

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Q: Find the derivative of the function. r sin(x) y = Jcos(x) In(4 + 9v) dv y'(x) = %3D

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Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: Find the derivative of F(x) = 4 n sin(t) dt. %3D dx 3x² cos(x)

A: Integral calculus is one of the two main parts of calculus that is concerned with the study of…

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Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find the derivative of y with respect to z. y In (sinh 3z) y -

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Q: Let y = In(x'e2x ). Find dy/dx.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of y=∫x4x√t√sin(t6)dt…

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Q: Find the derivative of F(x)

A: To Determine: find the derivative of F(x) Given: we have Fx=∫2x3costdt Explanation: we have a…

Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

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Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

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Q: Find the derivative of F(x) = n sin(t) dt. 3x2 d dx cos(x)

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Q: Find the derivative of y with respect to x. 6 y = (x³ In x) %3D dy dx II

A: Please see the below picture for detailed solution.

Q: Find the derivative of the following function. y= In (In (4x)) dy dx

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Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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

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Q: Find the derivative of the function In t dt.

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Q: Find the derivative of the function. 1 g(x) = dt Jtan(x) V2 +

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Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

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Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

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Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: 1. F(x) = S, t³ - 5t dt

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Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

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Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)