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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- 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

(s + 1) e^{- s π}

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

\int (0) d x

3 y^{^{'}} + 7 y = 4 e^{- x}

y = ln (6 (ln (x))^{8})

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