Let A(x) = f(t)dt, with f(x) shown in the graph below.

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: Part 4: A derivative computation using the FTC and the chain rule d d (F(2*)) = dx dt |3| e dx 20

A: Topic:- application of integration and derivatives

Q: * Part 4: A derivative computation using the FTC and the chain rule d d (F(x*) dx dt dx

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Q: Find the differential d4y of the function y=x5.

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Q: Compute the derivative of F(x) if F(x) = 9t dt F'(x) =

A: To find the derivative of integral, one have to use the fundamental law of calculus and substitute…

Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…

A: We have to find the derivative.

Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.

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Q: F(x) = f Cos t dt

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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: (a) Show that the derivative solution of this function y = x** is dy = x(**+x=1) [1+ x ln x (In x +…

A: The given function y=xxx Note:    Multiple questions are given, we are answered with only one…

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

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Q: Let F(x) = sin 3t dt, please find F'(0)

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Q: When is f (t) increasing at the greatest rate?

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Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x) = 2…

A: solution is given below

Q: Find the differential d3y of the function y=xsinhx.

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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: Find the derivative of F (x) = S (t3 – t)° dt. O 5( – t)* (3t2 – 1) - O (2 - 2) O 5(x³ – 2)* O 3t2 –…

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: Find the derivative. X dt 14) dx lol 0 5t+ 6

A: To find the derivative of given integral.

Q: Find the differential of the function. u = 2x +

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Q: Find the derivative of the function.

A: Given function is, F(x)=∫0e2xln(t+1)dt

Q: Find the differential d3y of the function y=x2ex.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

A: To find the derivative of the h(x) using fundamental theorem of calculus part 1.

Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: 3. Calculate the derivative of f(x) = tan(4t) dt. %3D -1/16

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Q: If z = (x + y) ev and x = 5t and y = 1 – t², find the following derivative using the chain rule.…

A: We are given that z=(x+y)ey,  x=5t, and y=1-t2. Now, we need to find dzdt.

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

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Q: Find the derivative df/dt. * f (t) = 2' + In (t)

A: Given f(t)= 2t+lnt

Q: se Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function g(x) : I VR+…

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Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

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

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Q: what is the difference is dt and dx in derivatives??

A: ‘dx’ is defined as differential which means a small change with respect to the variable x.‘dt’ is…

Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Find the derivative of the function. F(x) etd dt F'(x) =

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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: find the values of the derivatives ds/dt at t=-1 if s = 1 - 3t2

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Q: 1. F(x) = S, t³ - 5t dt

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h (x) =…

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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: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

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Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

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Q: Find the derivative of the given function a. F(x) = dt 1+ b. g(x) = [ - dt sinx 1+1*

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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)