Determine F(x) = J (x+1)dx x3+3x2+7x+5

Q: 1 Find the derivative of f(x) = V7+4x2 - 5.x2 +9

A: we apply chain rule in the first part and division rule in the second part

Q: 9. Find the first derivative: f(x) = 3ex %3D x2 (x+1)

A: Derivative of function

Q: Find the partial derivative. 3 (x² +3x-3y) 2.

A: Given  z = x2+3x-3y4 We have to find ∂z∂x.

Q: Compute the indicated derivative. d + 7x)(x2. dx x = 2

A:

Q: 5. Find the derivative of the function. f(x) = x°/1- 8x x(16-136x) 2/1-Sr x'(16+136x) f (x)3D 2/1-8x…

A: The function is given by,

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

A: The given function is, fx=x2+2x+2 To find the derivative of the function, we use the power rule of…

Q: What is the first derivative with respect to x of f(x) = (x² – 4) (3x – 2)? a. (2x)(3) b. 6х (x + 2)…

A:

Q: Find the derivative of the function. f(x) = V9 - 3x2 %D f'(x) %3D

A: The given function is f(x)=9-3x2

Q: 5. Find the derivative by using the quotient rule. 3x - 2 (a) 2x +3 V+2 (c)- 3+2x (b) x +1 x+2 (d):

A:

Q: Find the first and second derivatives of the functio f(x) = x(x² + 4)2 %3D f'(x) = %3D f" (x) = %3D

A:

Q: Find the derivative. f(x) = 5x2 + 6x + 9, find f'(x) %3D O 10x + 6 O 5x + 6 O 10x + 6 O 5x2 +6 W

A: Answer and explanation is given below....

Q: Find the second derivative of the functionf(x) 3Vx+2 2x+1

A: Given

Q: Find the first and the second derivatives of the function. f(x) = (8x + 8)³ f'(x) = f"(x) =| %3D

A:

Q: Determine the critical points of f(x) = x^2+8x+ 10 and apply the Second Derivative Test to find the…

A: Critical points are points where the function is defined and its derivative is zero or…

Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: 14. What is the first derivative of f (x) = (x²- 4)(3x - 2)? %3D a. 9x2- 4x – 12 С. 6х d. (x + 2)(x…

A: first derivative of f(x) = (x2 -4)(3x-2) f(x) = 3x3 -2x2-12x +8 now df(x)/dx = 9x2 -4x -12 so answer…

Q: 4 f(x) = Vx*+2 %3D x*-2

A:

Q: Find the derivative of f(x) = (x-2x)2 A) f'(x) = 6x5 - 12x3+ 8x B) f'(x) = 6x5- 16x3 + 8x %3D C)…

A: Here we find the derivatives of function.

Q: Find the second derivatives:y^n for y=1/8x^4-1/3x^3+3/4x^2-3x+5 And f(x)=2x/5x-2

A: (i): Given : y=18x4-13x3+34x2-3x+5 f(x)=2x5x-2…

Q: Find the derivative of f (x) = (x + 4)5 A) f'(x) = 5x (x* +4)* B) f'(x) = 6x (x+ 4)* C) f'(x) = 30x…

A:

Q: Find the derivative by using the quotient rule. 3x-2 (a) 2x +3 Jx +2 (c) x2 3+2x (b) x² +1 (d) *+2

A: Given: a)  3x−22x+3b)  3+2xx2+1c)  x+2x2d)  x+2x

Q: Find f' (x) using the rules for finding derivatives 4x2 – 7x +1 f(x): 2x + 9 f'(x)=O

A: To find The derivative of f(x)

Q: Find the first and second derivatives of the function. f(x) = (7x² + 6)7/2 r'(M) = | 49x(7x² + 6)…

A:

Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

A:

Q: 6. Use the quotient rule to find the derivative x - Vx y x + Vx (а) 8x2+ 2x y = x - 1 (b) 4х — 1 (c)…

A:

Q: Find the derivative. 2 f(x) = 6/6x +3 f'(x) =D %3D

A: Given : f(x) = 6√(6x2+3) Now we have find derivative of this

Q: Find the first and second derivatives of f(x). f(x) = 3x – 4x + 2 f'(x) = 2 9x – 4 f''(x)

A: Recall: dxndx =nxn-1.

Q: The derivative of f(x) = 9z3 12 8. is %3D 3z f'(x) O f(r) – 9x?+ 12x 4 – 9r– 12x + 8e 7 O f(r) - 9x…

A:

Q: 1. f(x) = V3x +2 2. f(x) = 2х-3. 4 %3D 5x+1

A: We know quotient rule of differentiation as follows  ddx{f(x)g(x)} = g(x) f'(x) - f(x) g'(x){ g(x)}2…

Q: Find the second derivative of y = Vx² +x-3 O 6/x O 12/x^5 O 6/x^2 O 12/x^3

A: dxndx =n.xn-1 dcdx =0 ; where, 'c' is an constant number.

Q: 2. Find the derivatives: (a) f(x)=(x² - 2x+1) (x² -1) x+2x+5 (b) f(x): %3D x² +1

A: Part (a) Given a function Using product rule of the derivative

Q: Find the first and second derivatives of the function. f(x) = 11x1 + 6x - x %3D f"(x) = f"(x) =

A:

Q: Find the derivative of f (x) = (x° – 4x (2² + - 8z – 2). %3D f' (z) =

A: We need to find the derivative of given function.

Q: Find the derivative for f (x) = V4 + e2x a. e2x /4+ e2x b. 1 2v2e2x xe2x-1 /4+ e2x C.

A: To find the derivative of fx=4+e2x.

Q: Find the second derivative of .2 y = Vx² + x-3 O 6/x^2 O 12/x^3 O 6/x O 12/x^5

A:

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: Find f(2x)dx if f(x)dx = 1. Enter the exact answer. f(2x)dx

A:

Q: Find the derivative. 18t5 dt dx O A. 6x5/2 - 6 В. 18х3 Oc. 9x2 O D. 12x5/2

A: We have to solve

Q: Test f(x) = (x3/3) +2x2-5x+1 for relative extrema, using the second-derivative test where possible.

A: For a given function,f(x), at relative extrema x=a, f'(a)=0.The second derivative test is applied to…

Q: 1) find the derivative of y = 4x2 – 3x – 2 | | then evaluate f'(x+3)

A:

Q: Find the first and second derivative 1. f(x) =x+6x-7x 2. f()=r-7 +2r 3. F(1)=(1+ 7r)

A:

Q: Find the derivative of the function. -5x3 + 3x + 2 y = dy -10x +3 - 2x2 dx dy -5x +3 + 2x2 dx -10 -…

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Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: 13: 3. y = V(4x + 3)3

A:

Q: What is the derivative of f(x)= e2x/ (3x+1)2

A: Given Function,fx = e2x3x+12

Q: Find the derivative of f(x) = e2" (3x² – x) %3D

A:

Q: • 5x²+1 (t²-t) dx F(x) =

A: