What is the derivative of f(x)=(x^2+5)(8-x) ?

The derivative of f(x)=(x^2+5)(8-x) is 16x-3x^2-5

What is the first derivative of f(x)=(x^2+5)(8-x) ?

The first derivative of f(x)=(x^2+5)(8-x) is 16x-3x^2-5

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derivative of

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

16 x - 3 x^{2} - 5

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (8 - x) = - 1

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

Simplify

2 x (8 - x) + (- 1) (x^{2} + 5) : 16 x - 3 x^{2} - 5

= 16 x - 3 x^{2} - 5

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What is the derivative of f(x)=(x^2+5)(8-x) ?
The derivative of f(x)=(x^2+5)(8-x) is 16x-3x^2-5
What is the first derivative of f(x)=(x^2+5)(8-x) ?
The first derivative of f(x)=(x^2+5)(8-x) is 16x-3x^2-5