f g is a differentiable function, find an expression for the derivative of each of the following functions. (a) y = xg(x) (b) y = xg'(x) xg'(x) + g(x) (x),6 − (x)6x g(x) - xg'(x) [g(x)]² (x)6 − (x),6x x² xg(x) + g'(x) x² X g(x) xg'(x) Exg'(x) + g(x) xg(x) - g'(x) g(x) - xg'(x) z[(x)6] xg'(x) = g(x) xg(x) + g'(x) x²

Q: Find the derivative a. f(x)= 6/(3x2-pi)4 b. f(x)=((3x2-pi x)4

A: (a) given,

Q: (b) F₂(x) = F₂'(x) = 9 4(x4 + 1)5 (d) F4(x) = F4'(x) = X 4 (c) F3(x) = (9x² + 1)5 4 F3'(x) = 9 (4x4…

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Q: Vx 3+x (g(x)) if g(x) = 3x +2 + S, * ** dx c) %3D

A: I applied Leibnitz rule

Q: If f(x) - g(x) = 1, then f and g have the same derivative. O True O False

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Q: Find the second derivative. f(x) = 5x10 - 19x5 – 11x3 + 2 f"(x) =

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Q: f(x) = 5x csc x 7 f (x) = 100 + 2cosx – 3x+x 3.

A: *formula:- d/dx (cscx) = -cscx*cotx. d/dx (x^{n}) = nx^{n-1}. d/dx (cosx) = -sinx.

Q: f(x)=(8x-1)(x2+4x+7)(x3-5) find the derivatives

A: fx=8x-1x2+4x+7x3-5 On simplification, we get…

Q: 4) Find the derivative of f(x) = (5x² - 3)² in two different ways.

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Q: Find the derivative of the function. y = (5x - 1)4(8x² - 1)-3 y' = 20(5x−1)3 (8x² - 1)³ 48(5x−1)4…

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Q: If f(x)=x2 -5x+7, calculate the derivative of f(x). Give it the name f'(x). Compare the domains of…

A: First we have to calculate the derivative of f(x) and then domains

Q: find the derivative of f(x) = (x² +4)(3x³-2x) at the point x =- 3[use product rule]

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Q: 2x2 – x +2 Find the derivative f'(x) by hand when f(x) = 12x + 7 f'(x) =

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Q: The derivative of the function f (x) = (x-1 – 2)(3 – Vx ) is, %3D 2x2 – x – 6/x A. fi(x) %3D 2x2+…

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Q: What rule do you use to calculate the derivative of f(x) = exx2 and f(x)=(x2-3x+1)/(x+5) ?

A: Use the product rule and quotient rule of derivative:

Q: Y=0.83x +0.0094x2 +0.000042x3 Take out derivative of the given function.

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Q: evaluate the derivative of the function at the given pointf(x)=-4/(2x2-3x)4 , (1,-4)

A: