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-2^2)

Solution

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

Solution

5 x^{4} - 16 x^{3} + 12 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 x^{2} (x - 2)^{2} + 2 (x - 2) x^{3} : 5 x^{4} - 16 x^{3} + 12 x^{2}

= 5 x^{4} - 16 x^{3} + 12 x^{2}

Graph

Popular Examples

integral of \sqrt[3]{x}*(x+1)^2

\int 3 x \cdot (x + 1)^{2} d x

(1+y^2+xy^2)dx+(x^2y+y+2xy)dy=0

(1 + y^{2} + x y^{2}) d x + (x^{2} y + y + 2 x y) d y = 0

derivative of x^{0.6}

\frac{d}{d x} (x^{0.6})

area y=x,y=12x,x=9 area

y = x, y = 12 x, x = 9

laplacetransform 5x laplace transform

5 x

Frequently Asked Questions (FAQ)

What is the derivative of x^3(x-2^2) ?
The derivative of x^3(x-2^2) is 5x^4-16x^3+12x^2
What is the first derivative of x^3(x-2^2) ?
The first derivative of x^3(x-2^2) is 5x^4-16x^3+12x^2