What is the derivative of {f}(x(x)^2) ?

The derivative of {f}(x(x)^2) is derivative of {f}(x)x^2+2x{f}(x)

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

The first derivative of {f}(x(x)^2) is derivative of {f}(x)x^2+2x{f}(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

f = f (x), g = x^{2}

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

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

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

\frac{d y}{d x} = \frac{y ^{2}}{x ^{2}} + \frac{y}{x} + 1

\frac{d}{d x} (\frac{x ^{2} - 10 x + 2}{x ( x ^{2} - 1 )})

\frac{d}{d x} (\frac{x ^{5}}{3 - x ^{4}})

\frac{d}{d x} (\frac{sin ^{2} ( x )}{4})

\frac{d}{d x} (e^{x} ln (x^{2}))

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