en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of g(x)=x^2(1-5x)

Solution

derivative of

g (x) = x^{2} (1 - 5 x)

Solution

2 x - 15 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (1 - 5 x))

Apply the Product Rule:

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

f = x^{2}, g = 1 - 5 x

= \frac{d}{d x} (x^{2}) (1 - 5 x) + \frac{d}{d x} (1 - 5 x) x^{2}

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

\frac{d}{d x} (1 - 5 x) = - 5

= 2 x (1 - 5 x) + (- 5) x^{2}

Simplify

2 x (1 - 5 x) + (- 5) x^{2} : 2 x - 15 x^{2}

= 2 x - 15 x^{2}

Popular Examples

f(x)=(2x^2-1)/(x^3-x)

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

(\partial)/(\partial x)(2z^3-3(x^2+y^2)z)

\frac{\partial}{\partial x} (2 z^{3} - 3 (x^{2} + y^{2}) z)

limit as x approaches-8+of x/(x+8)

x \to - 8 + lim (\frac{x}{x + 8})

(\partial)/(\partial x)(6x^3y+6y^5+1)

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

d/(dv)(sqrt(v-1))

\frac{d}{d v} (v - 1)

Frequently Asked Questions (FAQ)

What is the derivative of g(x)=x^2(1-5x) ?
The derivative of g(x)=x^2(1-5x) is 2x-15x^2
What is the first derivative of g(x)=x^2(1-5x) ?
The first derivative of g(x)=x^2(1-5x) is 2x-15x^2