en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2(x-1^3)

Solution

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

Solution

2 x (x - 1)^{3} + 3 (x - 1)^{2} x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = (x - 1)^{3}

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

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

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

= 2 x (x - 1)^{3} + 3 (x - 1)^{2} x^{2}

Popular Examples

limit as x approaches 0 of ((2.8^x-1))/x

x \to 0 lim (\frac{( 2. 8 ^{x} - 1 )}{x})

integral from 0 to 1/2 of sqrt(1-4x^2)

\int_{0}^{\frac{1}{2}} 1 - 4 x^{2} d x

integral of 6/(xsqrt(x^2+1))

\int \frac{6}{x x ^{2} + 1} d x

integral of (x+1)e^{9x^2+18x}

\int (x + 1) e^{9 x^{2} + 18 x} d x

(d^2y)/(dx^2)-4(dy)/(dx)+13y=8sin(3x),y(0)=1,y^'(0)=2

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 13 y = 8 sin (3 x), y (0) = 1, y^{^{'}} (0) = 2

Frequently Asked Questions (FAQ)

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