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Popular >

derivative of (x^2+8)(5-x)

Solution

derivative of

(x^{2} + 8) (5 - x)

Solution

10 x - 3 x^{2} - 8

Solution steps

\frac{d}{d x} ((x^{2} + 8) (5 - x))

Apply the Product Rule:

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

f = x^{2} + 8, g = 5 - x

= \frac{d}{d x} (x^{2} + 8) (5 - x) + \frac{d}{d x} (5 - x) (x^{2} + 8)

\frac{d}{d x} (x^{2} + 8) = 2 x

\frac{d}{d x} (5 - x) = - 1

= 2 x (5 - x) + (- 1) (x^{2} + 8)

Simplify

2 x (5 - x) + (- 1) (x^{2} + 8) : 10 x - 3 x^{2} - 8

= 10 x - 3 x^{2} - 8

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2+8)(5-x) ?
The derivative of (x^2+8)(5-x) is 10x-3x^2-8
What is the first derivative of (x^2+8)(5-x) ?
The first derivative of (x^2+8)(5-x) is 10x-3x^2-8