For the function f(x) = 4x3, find f'(2). %3D

Q: Use the fact that e4x = (ex)4 to find d/dx(e4x). Simplify the derivative as much as possible.

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: Find for the following functions: - dx 3x2-4x+4 1) y = %3| Z

A: dydx is called the derivative of function y.Derivatives of polynomials are :→dxndx =…

Q: Find the indicated derivative. 32 df If f(x) =F + 12 x, find dx x = 4 df dx x = 4

A: Topic:- Derivatives

Q: Find the derivative of the function. f(x) = V 5x + 4

A: Question number 1,Given,          fx=5x+4

Q: Differentiate the function. y = V 3x2 + 8x + 1 dy dx

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Q: find dy/dx for each function. 228.  y=(3x^2+3x−1)^4

A: The given function y=3x2+3x-14 Differentiate both sideds with respect to x using chain rule…

Q: Find for the function y = 3*. dx dy dx 11

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Q: f(x) = xe (1+e*)

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Q: x – 8 dx x² – x – 6

A: Find the integral by substitution method

Q: constant

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Q: z is jointly proportional to x3 and y3. If z=490 when x=8 and y=4, find z when x=6 and y=5. (Round…

A: z is jointly proportional to x3 and y3. So,   z  ∝  x3y3 z = kx3y3

Q: Find the antiderivative for each function when C equals 0. Do as many as you can mentally. Check…

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Q: Find the derivative and simplify A. y =((x2)/(2 + lnx)) B. f(x) = ln (√((4x + 1)/(5x + 7))

A: We have to find

Q: 1+x dx V1-x

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Q: Find for y = dx dx X [11tªdt. 0

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Q: Find the indicated derivative. df If f(x) = x3, find dx 8 df dx |x = -11 || X 32 X = 10 X 1 2 11

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Q: S(8x3 + x-3)dx

A: Solve by integration

Q: Evaluate. (Use C for the constant of integration.) x2 dx (1 – 25x²)3/2

A: Given,          ∫x21-25x232dx

Q: B. Find the indicated derivative. (15 pts) -4 y =;y(3) 2. x2 – 4y2 = 5; y" x2 -

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Q: x dx 1) S 1-2x

A: As there are multiple questions, 1)  is solved here.

Q: If fſ f (x)dx = 8, what would f f(x)dx equal?

A: Given, the definite integral gives result 8. Concept - when the limits of integration is changed…

Q: If  f '(x) = x4,  what is f(x)? (Use C for the constant of integration.)

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Q: (b) Given [f(x)dx = 21 f (x)dx = 29, find the value of S. 25 (x)dx . and

A: ∫102f(x)dx=21∫107f(x)dx=29

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: L V9 – x² dx

A: Given,          ∫039-x2dx

Q: S fAx)dx=10 and | f(x)dx=3, then (4 – x)dx=? -

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Q: _xe. f(x) = (1+e*)

A: Here we have to find the differentiation of given function. The solution is following.

Q: For the demand equation, use implicit differentiation to find  dp/dx. 17p2 + 5p + 6 = x

A: Given:

Q: If f(x) dx = 3 and f(x) dx = 4 what is the value of %3D 5f(x) dx?

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Q: 7) I = fx v-4 dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2x Using the definition of derivative, find Given y = dy %3D x+8 dx

A: dy/dx from definition of derivative is given below

Q: Find the indicated derivative. If y = x5 – x/2, find d?y dx2 d?y x2 %3D dx

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Q: - Trig Sub 1 dx V9 – x²

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Q: If f(x)=3^x x^3, what is dy/dx?

A: Solution: Here  f(x)=3xx3

Q: Evaluate dy for f(x)= (square root of x) +3 where x=9 and dx=0.12

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Q: dx 6) I = v9-

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: SOLVE TOTAL DIFF.. EQUATION. (x+2)²dy + y² (dx+dz) =0

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Q: (x) dx = 6 and f(x) dx = 10 , then +3] dx = %3D 2

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Q: Find the value of (x)) dx if f(x) dx=11 and f(x) dx=3.

A: here we have to find the integral vaule

Q: Q3/ find the derivative La)= メ 2. logs (x+3) 2x+4

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Q: Evaluate. (Use C for the constant of integration.) x3 + 25 dx x2 + 25

A: Given that: ∫x3+25x2+25dx

Q: Find the antiderivative of the function 4x3 - 2x2 +x - 5 dx

A: This question is based on indefinite integral.

Q: Q7/ find the derivative (, df. 1 f(x) = + 5 e* x4/3

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Q: f(x)dx=10 and | f(x)dx=3, then f(4 – x)dx=?

A: topic - properties of integration

Q: Suppose y' is proportional to y and y(0) = 10 and y(1) = 20. For what value of t does y(t) = 25?…

A: Differential equation variable separable

Q: If | f{x)dx=12, what is the value of f(6 – x)dx?

A: The solution is,  ∫06f(6-x) dx =12

Q: x2 — х + 36 dx х3 + 6х

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Q: y is inversely proportional to Vx y = 4 when x= 9 Work out an equation connecting y and x.

A: We have to write an equation connecting y and x for the given conditions: y is inversely…