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^3))

Solution

\frac{d}{d x} (f (x) (x^{3}))

Solution

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

Solution steps

\frac{d}{d x} (f (x) (x^{3}))

Apply the Product Rule:

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

f = f (x), g = x^{3}

= \frac{d}{d x} (f (x)) x^{3} + \frac{d}{d x} (x^{3}) f (x)

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

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

Popular Examples

integral of (2e^{2x})/(2+e^{2x)}

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

limit as x approaches 0 of e^{9x}

x \to 0 lim (e^{9 x})

limit as x approaches-1 of (2/3)^x

x \to - 1 lim ((\frac{2}{3})^{x})

f(x)=(e^x)/(1-e^{-x)}

f (x) = \frac{e ^{x}}{1 - e ^{- x}}

integral from 1/2 to 3 of 4xln(2x)

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

Frequently Asked Questions (FAQ)

What is the derivative of {f}(x(x^3)) ?
The derivative of {f}(x(x^3)) is derivative of {f}(x)x^3+3x^2{f}(x)
What is the first derivative of {f}(x(x^3)) ?
The first derivative of {f}(x(x^3)) is derivative of {f}(x)x^3+3x^2{f}(x)