en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of f(x)=x^2(x^2+1)

Solution

derivative of

f (x) = x^{2} (x^{2} + 1)

Solution

4 x^{3} + 2 x

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = x^{2} + 1

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

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

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

= 2 x (x^{2} + 1) + 2 x x^{2}

Simplify

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

= 4 x^{3} + 2 x

Graph

Popular Examples

(\partial)/(\partial y)(xe^{-x^2-y^2})

\frac{\partial}{\partial y} (x e^{- x^{2} - y^{2}})

integral from 0 to 4 of xsqrt(16-x^2)

\int_{0}^{4} x 16 - x^{2} d x

integral of (1-t)/t

\int \frac{1 - t}{t} d t

y^{''}-6y^'+13y=0,y(0)=0,y^'(0)=-3

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3

derivative of \sqrt[3]{sin^2(2x})

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

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^2(x^2+1) ?
The derivative of f(x)=x^2(x^2+1) is 4x^3+2x
What is the first derivative of f(x)=x^2(x^2+1) ?
The first derivative of f(x)=x^2(x^2+1) is 4x^3+2x