en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (1+6x^2(x-x^2))

Solution

\frac{d}{d x} ((1 + 6 x^{2}) (x - x^{2}))

Solution

- 24 x^{3} + 18 x^{2} - 2 x + 1

Solution steps

\frac{d}{d x} ((1 + 6 x^{2}) (x - x^{2}))

Apply the Product Rule:

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

f = 1 + 6 x^{2}, g = x - x^{2}

= \frac{d}{d x} (1 + 6 x^{2}) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (1 + 6 x^{2})

\frac{d}{d x} (1 + 6 x^{2}) = 12 x

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

= 12 x (x - x^{2}) + (1 - 2 x) (1 + 6 x^{2})

Simplify

12 x (x - x^{2}) + (1 - 2 x) (1 + 6 x^{2}) : - 24 x^{3} + 18 x^{2} - 2 x + 1

= - 24 x^{3} + 18 x^{2} - 2 x + 1

Graph

Popular Examples

integral of xcsch^2((x^2)/2)

\int x csch^{2} (\frac{x ^{2}}{2}) d x

area x=2y^2,x=y^2+4 area

x = 2 y^{2}, x = y^{2} + 4

integral of (cos(x))^6

\int (cos (x))^{6} d x

derivative of ((x^2-1))/((x^2+x+1))derivative of

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

(\partial)/(\partial x)(z-x)

\frac{\partial}{\partial x} (z - x)

Frequently Asked Questions (FAQ)

What is the derivative of (1+6x^2(x-x^2)) ?
The derivative of (1+6x^2(x-x^2)) is -24x^3+18x^2-2x+1
What is the first derivative of (1+6x^2(x-x^2)) ?
The first derivative of (1+6x^2(x-x^2)) is -24x^3+18x^2-2x+1