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Popular >

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

Solution

derivative of

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

Solution

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

Popular Examples

integral of (2x)/(1+4x^2)

\int \frac{2 x}{1 + 4 x ^{2}} d x

derivative of 6/(x^3)derivative of

\frac{6}{x ^{3}}

integral of (3x^2)/(4sqrt(5-x^3))

\int \frac{3 x ^{2}}{4 5 - x ^{3}} d x

tangent of f(x)=3x^2-3x,\at x=3 tangent of

f (x) = 3 x^{2} - 3 x, at x = 3

limit as x approaches 0 of (sinh(x))/x

x \to 0 lim (\frac{sinh ( x )}{x})

Frequently Asked Questions (FAQ)

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