What is the derivative of (4x^2+x(x-x^2)) ?

The derivative of (4x^2+x(x-x^2)) is -16x^3+9x^2+2x

What is the first derivative of (4x^2+x(x-x^2)) ?

The first derivative of (4x^2+x(x-x^2)) is -16x^3+9x^2+2x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} ((4 x^{2} + x) (x - x^{2}))

- 16 x^{3} + 9 x^{2} + 2 x

Solution steps

\frac{d}{d x} ((4 x^{2} + x) (x - x^{2}))

Apply the Product Rule:

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

f = 4 x^{2} + x, g = x - x^{2}

= \frac{d}{d x} (4 x^{2} + x) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (4 x^{2} + x)

\frac{d}{d x} (4 x^{2} + x) = 8 x + 1

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

= (8 x + 1) (x - x^{2}) + (1 - 2 x) (4 x^{2} + x)

Simplify

(8 x + 1) (x - x^{2}) + (1 - 2 x) (4 x^{2} + x) : - 16 x^{3} + 9 x^{2} + 2 x

= - 16 x^{3} + 9 x^{2} + 2 x

\int_{0}^{3} 5 x - x^{2} - 2 x d x

\frac{1}{9 x ^{\frac{8}{9}}}

\int x csc (4) x^{2} d x

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

f (x) = x^{3}

What is the derivative of (4x^2+x(x-x^2)) ?
The derivative of (4x^2+x(x-x^2)) is -16x^3+9x^2+2x
What is the first derivative of (4x^2+x(x-x^2)) ?
The first derivative of (4x^2+x(x-x^2)) is -16x^3+9x^2+2x