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Popular >

derivative of (x+3)(x-5)^7

Solution

derivative of

(x + 3) (x - 5)^{7}

Solution

(x - 5)^{7} + 7 (x - 5)^{6} (x + 3)

Solution steps

\frac{d}{d x} ((x + 3) (x - 5)^{7})

Apply the Product Rule:

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

f = x + 3, g = (x - 5)^{7}

= \frac{d}{d x} (x + 3) (x - 5)^{7} + \frac{d}{d x} ((x - 5)^{7}) (x + 3)

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

\frac{d}{d x} ((x - 5)^{7}) = 7 (x - 5)^{6}

= 1 \cdot (x - 5)^{7} + 7 (x - 5)^{6} (x + 3)

Simplify

= (x - 5)^{7} + 7 (x - 5)^{6} (x + 3)

Popular Examples

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Frequently Asked Questions (FAQ)

What is the derivative of (x+3)(x-5)^7 ?
The derivative of (x+3)(x-5)^7 is (x-5)^7+7(x-5)^6(x+3)
What is the first derivative of (x+3)(x-5)^7 ?
The first derivative of (x+3)(x-5)^7 is (x-5)^7+7(x-5)^6(x+3)