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Popular >

derivative of y=((x+1)(x-3)^3)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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