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+8x}

Solution

derivative of

Solution

\frac{8}{3 ( 1 + 8 x ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 8 x)

= \frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 8 x)

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

= \frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \cdot 8

Simplify

\frac{1}{3 ( 1 + 8 x ) ^{\frac{2}{3}}} \cdot 8 : \frac{8}{3 ( 1 + 8 x ) ^{\frac{2}{3}}}

= \frac{8}{3 ( 1 + 8 x ) ^{\frac{2}{3}}}

Popular Examples

integral of (x^2+2x)/(sqrt(x^3+3x^2+2))

\int \frac{x ^{2} + 2 x}{x ^{3} + 3 x ^{2} + 2} d x

y^{''}-y=t^2e^t

y^{^{''}} - y = t^{2} e^{t}

integral of (x^2)/(sqrt(x^3))

\int \frac{x ^{2}}{x ^{3}} d x

(dy)/((6+y)^2)=(dx)/((10+9x)^4)

\frac{d y}{( 6 + y ) ^{2}} = \frac{d x}{( 10 + 9 x ) ^{4}}

(df)/(dθ)=sin(θ)+csc(θ)

\frac{df}{d θ} = sin (θ) + csc (θ)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=\sqrt[3]{1+8x} ?
The derivative of f(x)=\sqrt[3]{1+8x} is 8/(3(1+8x)^{2/3)}
What is the first derivative of f(x)=\sqrt[3]{1+8x} ?
The first derivative of f(x)=\sqrt[3]{1+8x} is 8/(3(1+8x)^{2/3)}