en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

5 x^{4} - 8 x^{3} + 3 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 x^{2} (x - 1)^{2} + 2 (x - 1) x^{3} : 5 x^{4} - 8 x^{3} + 3 x^{2}

= 5 x^{4} - 8 x^{3} + 3 x^{2}

Popular Examples

tangent of y=(3sqrt(x)+x)(2-x^2)tangent of

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

derivative of f(x)=(x-7)/(-5x-10)derivative of

f (x) = \frac{x - 7}{- 5 x - 10}

derivative of sqrt(13x^2-5x+8)

\frac{d}{d x} (13 x^{2} - 5 x + 8)

7y^'+1y=8e^3x,y(0)=9

7 y^{^{'}} + 1 y = 8 e^{3} x, y (0) = 9

f(x)=sin(3x)cos(5x)

f (x) = sin (3 x) cos (5 x)

Frequently Asked Questions (FAQ)

What is the derivative of x^3(x-1^2) ?
The derivative of x^3(x-1^2) is 5x^4-8x^3+3x^2
What is the first derivative of x^3(x-1^2) ?
The first derivative of x^3(x-1^2) is 5x^4-8x^3+3x^2