What is the derivative of y=(1+6x^2)(x-x^2) ?

The derivative of y=(1+6x^2)(x-x^2) is -24x^3+18x^2-2x+1

What is the first derivative of y=(1+6x^2)(x-x^2) ?

The first derivative of y=(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 >

derivative of

y = (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

n = 1 \sum \infty \frac{5}{n ^{4}}

x \to \infty lim (\frac{x}{3 x})

\frac{d ^{2}}{d x ^{2}} (\frac{1}{4 x ^{2} + 5 x})

\frac{d}{d x} (cos (7 - 2 x))

\frac{d}{d x} (e^{x} (x \cdot sin (x) + (1 - x) \cdot cos (x)))

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