What is the derivative of (1+8x^2)(x-x^2) ?

The derivative of (1+8x^2)(x-x^2) is -32x^3+24x^2-2x+1

What is the first derivative of (1+8x^2)(x-x^2) ?

The first derivative of (1+8x^2)(x-x^2) is -32x^3+24x^2-2x+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

f = 1 + 8 x^{2}, g = x - x^{2}

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

\frac{d}{d x} (1 + 8 x^{2}) = 16 x

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

= 16 x (x - x^{2}) + (1 - 2 x) (1 + 8 x^{2})

Simplify

16 x (x - x^{2}) + (1 - 2 x) (1 + 8 x^{2}) : - 32 x^{3} + 24 x^{2} - 2 x + 1

= - 32 x^{3} + 24 x^{2} - 2 x + 1

d x + e^{4 x} d y = 0

\int \frac{8 ( x ^{2} + 1 )}{4 x ^{2} + 9} d x

\frac{1 + 6 s ^{2}}{s ( s ^{2} + 1 )}

\frac{d ^{2} y}{d x ^{2}} = (4 sin (3 x))

What is the derivative of (1+8x^2)(x-x^2) ?
The derivative of (1+8x^2)(x-x^2) is -32x^3+24x^2-2x+1
What is the first derivative of (1+8x^2)(x-x^2) ?
The first derivative of (1+8x^2)(x-x^2) is -32x^3+24x^2-2x+1