en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

y^{''}+36y=-24sin(6t)

y^{^{''}} + 36 y = - 24 sin (6 t)

(x e^{x})^{^{'}}

(e^x+y)dx+(e^y+x)dy=0

(e^{x} + y) d x + (e^{y} + x) d y = 0

(\partial)/(\partial x)(2xsin(y))

\frac{\partial}{\partial x} (2 x sin (y))

derivative of (x-1^{1/2})

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

Frequently Asked Questions (FAQ)

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