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)=\sqrt[3]{1+4x}

Solution

derivative of

Solution

\frac{4}{3 ( 1 + 4 x ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 4 x)

= \frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 4 x)

\frac{d}{d x} (1 + 4 x) = 4

= \frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \cdot 4

Simplify

\frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \cdot 4 : \frac{4}{3 ( 1 + 4 x ) ^{\frac{2}{3}}}

= \frac{4}{3 ( 1 + 4 x ) ^{\frac{2}{3}}}

Popular Examples

integral from 2 to 3 of 4e^{4x}

\int_{2}^{3} 4 e^{4 x} d x

y^{^{'}} + 3 y = t e^{4 t}

integral from 16 to 25 of (sqrt(x-16))/x

\int_{16}^{25} \frac{x - 16}{x} d x

integral of cos(x)(8+5sin^2(x))

\int cos (x) (8 + 5 sin^{2} (x)) d x

integral of 1/(x^2+6x+8)

\int \frac{1}{x ^{2} + 6 x + 8} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=\sqrt[3]{1+4x} ?
The derivative of f(x)=\sqrt[3]{1+4x} is 4/(3(1+4x)^{2/3)}
What is the first derivative of f(x)=\sqrt[3]{1+4x} ?
The first derivative of f(x)=\sqrt[3]{1+4x} is 4/(3(1+4x)^{2/3)}