Differentiate. f(x) = 3x(5x + 4)° O A. f'(x) = 3(5x+ 4) (20x + 4) O B. f'(x) = 3(20x + 4) OC. f(x) = 3(5x + 4) O D. f'(x) = 3(5x +4)°(8x + 4)

Q: Differentiate. ax + b f(x) %3D Cx + d f '(x) =

A:

Q: 4 X- - 5x +4. %3D Find f'(x), f"(x), and f (x) for f(x) = f'(x) = f"(x) =

A:

Q: 9-x2 x dx

A: ∫9-x2x2dx=∫cot2udu=∫ -1+csc2udu=-∫ 1du+∫csc2udu=-u-cotuSubstitute back…

Q: Simplify: x + 1 x - 1 x - 1 x + 1 x - 1 x + 1' x + 1 x - 1

A:

Q: ƒ' (4) = If f(x) = 3√√√x(x³ − 2√x + 2), find f'(4).

A: Given that

Q: Find y'. y = (x² - 2x+2)(2x³ - x²+4) OA. 10x4 - 20x³ + 18x² + 4x-8 OB. 10x4 - 16x³ + 18x² + 4x-8 O…

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Q: x - x +2 4. If flx) =x + 7 find f'(x) . (5x - 1) (3x²) (A) (x' + 7)(5x - 1) – (x° – x + 2)(3x²) (B)…

A: The given function is  f(x) = x5-x+2x3+7

Q: 9. f²-2x(3x - 1) dx

A:

Q: (2x+3) 8. S- (x2 +x+2)2

A: Let's find.

Q: (2x + 1)3 (1- 4x)2' find f'(x) and fully simplify. If f (x) =

A: fx=2x+131-4x2f'x=ddx2x+131-4x2

Q: y" - 8y + 25y = 0; y(0) = 0, y'(0) = 3

A: y''-8y'+25y=0; y(0)=0, y'(0)=3 We have to solve it using Laplace transform.

Q: y=3x+4 / 2x+1 y`(0)=?

A:

Q: Find f'(x) and simplify. x²+2 7x-8 f(x) = Which of the following shows the correct application of…

A: I have explained everything with in the solution. Please go through that.

Q: y=x^2+2x+1 / x^2-2x+1 is equal to y'= -4(x+1) / (x-1)^3  True or False?

A: Simply and differentiate to get the answer.

Q: V(x) = (5x³ + 3)(x* – 2x) V'(x)

A:

Q: If 87 + 2 f(x) + 3x² (ƒ(x))³ = 0 and ƒ(1) = −3, find ƒ'(1).

A: 87+2f(x)+3x2(f(x))3=0,f(1)=−3

Q: 01/ Evaluste the following integrals (four 9-x2 secx da O Sex dx secx ,dx *(x+2) * 4x-16

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: Differentiate. y = ³√√x³+3x+1.x4

A: Given function y = x3 + 3x + 13.x4

Q: Determine the particular solution of the ODE y” + lnx = -1 a. (-0.5 * lnx) + 0.25x b. (0.5x^2 * lnx)…

A:

Q: ① -2) (7x 0 - 3x - 2 + 이승 이승 ② 1 ( + ex) 2 dx Hx2

A: (1)ddx(7x6+3x4−2x)

Q: Find y'' for y = 5x +4. 25x2 y'= - O A. 2 (5x? +4) 1 y" = O B. 4 (5x2 + 4) 20 y" = OC. (5x? + 4)…

A:

Q: Find f'(x) and simplify. f(x) = (0.2x + 2)(0.6x - 9) Which of the following shows the correct…

A: f(x)= (0.2x+2)(0.6x-9)

Q: Find L'} se 's²+4'

A: In the given question we have to find the Laplace inverse transformation of the given function f(s)…

Q: Find y'. y=x V6x - 1

A:

Q: 215tandx= Q2 2x+ 1

A: Given: 1) ∫tan-1xdx2) ∫2x3+1x4+2x+1dx

Q: 2. Sx³(a² + x²)° dx ? + x?)% dx

A: Using property of integration,

Q: Evaluate les-). d 3x dx OA (3x³- x?)e3x²-x?-1 O A. ² – x² – 1 OB. O B, e oc (9x² - 2x)e³x³-x? OC.…

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Q: If f(x) = 6 + 6x − 4x², find ƒ'(-3). - -48 X

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Q: 2. Prove that d [(2x+1)³] (2x+1)³(4x-19) (x-3)² dx = Then, -5 (2x+1)(8x-38) 3(x-3)² dx.

A: