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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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