What is the derivative of f(x)=(x-2)^3(x+1)^2 ?

The derivative of f(x)=(x-2)^3(x+1)^2 is 3(x-2)^2(x+1)^2+2(x+1)(x-2)^3

What is the first derivative of f(x)=(x-2)^3(x+1)^2 ?

The first derivative of f(x)=(x-2)^3(x+1)^2 is 3(x-2)^2(x+1)^2+2(x+1)(x-2)^3

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derivative of

f (x) = (x - 2)^{3} (x + 1)^{2}

3 (x - 2)^{2} (x + 1)^{2} + 2 (x + 1) (x - 2)^{3}

Solution steps

\frac{d}{d x} ((x - 2)^{3} (x + 1)^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x - 2)^{3}, g = (x + 1)^{2}

= \frac{d}{d x} ((x - 2)^{3}) (x + 1)^{2} + \frac{d}{d x} ((x + 1)^{2}) (x - 2)^{3}

\frac{d}{d x} ((x - 2)^{3}) = 3 (x - 2)^{2}

\frac{d}{d x} ((x + 1)^{2}) = 2 (x + 1)

= 3 (x - 2)^{2} (x + 1)^{2} + 2 (x + 1) (x - 2)^{3}

\frac{d}{d x} (e^{x} cos (5 x))

\frac{d}{d x} (A x e^{2 x})

f (x) = x + 1, (8, 3)

\int \frac{4 x ^{2} - 64}{x} d x

What is the derivative of f(x)=(x-2)^3(x+1)^2 ?
The derivative of f(x)=(x-2)^3(x+1)^2 is 3(x-2)^2(x+1)^2+2(x+1)(x-2)^3
What is the first derivative of f(x)=(x-2)^3(x+1)^2 ?
The first derivative of f(x)=(x-2)^3(x+1)^2 is 3(x-2)^2(x+1)^2+2(x+1)(x-2)^3