en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x{z}(x(x)^2)

Solution

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

Solution

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

Solution steps

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

Simplify

x z (x) (x)^{2} : x^{3} z (x)

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

Apply the Product Rule:

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

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

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

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

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

Popular Examples

derivative of 9/(5x^2)

\frac{d}{d x} (\frac{9}{5 x ^{2}})

integral of 10cos^3(x)

\int 10 cos^{3} (x) d x

derivative of f(x)= 4/(8x+7)derivative of

f (x) = \frac{4}{8 x + 7}

limit as x approaches 0 of (8sin(3x))/(1-cos(3x))

x \to 0 lim (\frac{8 sin ( 3 x )}{1 - cos ( 3 x )})

derivative of 2e^{2x}x+e^{2x}

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

Frequently Asked Questions (FAQ)

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