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)=8sqrt(6x^2+7)

Solution

derivative of

f (x) = 8 6 x^{2} + 7

Solution

\frac{48 x}{6 x ^{2} + 7}

Solution steps

\frac{d}{d x} (8 6 x^{2} + 7)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (6 x^{2} + 7)

Apply the chain rule:

\frac{1}{2 6 x ^{2} + 7} \frac{d}{d x} (6 x^{2} + 7)

= \frac{1}{2 6 x ^{2} + 7} \frac{d}{d x} (6 x^{2} + 7)

\frac{d}{d x} (6 x^{2} + 7) = 12 x

= 8 \cdot \frac{1}{2 6 x ^{2} + 7} \cdot 12 x

Simplify

8 \cdot \frac{1}{2 6 x ^{2} + 7} \cdot 12 x : \frac{48 x}{6 x ^{2} + 7}

= \frac{48 x}{6 x ^{2} + 7}

Popular Examples

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

\int (\frac{x + 2}{x ^{2} + 4 x}) d x

derivative of (6x^2+8x+2/(sqrt(x)))

\frac{d}{d x} (\frac{6 x ^{2} + 8 x + 2}{x})

integral of (7x)/((x^2+2)^2)

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

(\partial)/(\partial y)(xycos(z))

\frac{\partial}{\partial y} (x y cos (z))

integral of sin(xy)

\int sin (x y) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=8sqrt(6x^2+7) ?
The derivative of f(x)=8sqrt(6x^2+7) is (48x)/(sqrt(6x^2+7))
What is the first derivative of f(x)=8sqrt(6x^2+7) ?
The first derivative of f(x)=8sqrt(6x^2+7) is (48x)/(sqrt(6x^2+7))