en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(x^2+8)(7-x)

Solution

derivative of

f (x) = (x^{2} + 8) (7 - x)

Solution

14 x - 3 x^{2} - 8

Solution steps

\frac{d}{d x} ((x^{2} + 8) (7 - x))

Apply the Product Rule:

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

f = x^{2} + 8, g = 7 - x

= \frac{d}{d x} (x^{2} + 8) (7 - x) + \frac{d}{d x} (7 - x) (x^{2} + 8)

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

\frac{d}{d x} (7 - x) = - 1

= 2 x (7 - x) + (- 1) (x^{2} + 8)

Simplify

2 x (7 - x) + (- 1) (x^{2} + 8) : 14 x - 3 x^{2} - 8

= 14 x - 3 x^{2} - 8

Popular Examples

limit as x approaches 1 of e^{1/(x-1)}

x \to 1 lim (e^{\frac{1}{x - 1}})

integral of (4x)/(sqrt(3x))

\int \frac{4 x}{3 x} d x

integral from 1 to 4 of 2/(x^2)

\int_{1}^{4} \frac{2}{x ^{2}} d x

derivative of sin^6(pix)

\frac{d}{d x} (sin^{6} (π x))

integral of (x^2+x)/((x-3)(x^2+1))

\int \frac{x ^{2} + x}{( x - 3 ) ( x ^{2} + 1 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2+8)(7-x) ?
The derivative of f(x)=(x^2+8)(7-x) is 14x-3x^2-8
What is the first derivative of f(x)=(x^2+8)(7-x) ?
The first derivative of f(x)=(x^2+8)(7-x) is 14x-3x^2-8