What is the derivative of f(x)=(1+7x^2)(x-x^2) ?

The derivative of f(x)=(1+7x^2)(x-x^2) is -28x^3+21x^2-2x+1

What is the first derivative of f(x)=(1+7x^2)(x-x^2) ?

The first derivative of f(x)=(1+7x^2)(x-x^2) is -28x^3+21x^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

f (x) = (1 + 7 x^{2}) (x - x^{2})

- 28 x^{3} + 21 x^{2} - 2 x + 1

Solution steps

\frac{d}{d x} ((1 + 7 x^{2}) (x - x^{2}))

Apply the Product Rule:

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

f = 1 + 7 x^{2}, g = x - x^{2}

= \frac{d}{d x} (1 + 7 x^{2}) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (1 + 7 x^{2})

\frac{d}{d x} (1 + 7 x^{2}) = 14 x

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

= 14 x (x - x^{2}) + (1 - 2 x) (1 + 7 x^{2})

Simplify

14 x (x - x^{2}) + (1 - 2 x) (1 + 7 x^{2}) : - 28 x^{3} + 21 x^{2} - 2 x + 1

= - 28 x^{3} + 21 x^{2} - 2 x + 1

(3, - 5), (8, 4)

\frac{d}{d x} (cos (\frac{1 - e ^{3 x}}{1 + e ^{3 x}}))

y^{^{'}} + 3 y = t + e^{- 2 t}

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

y^{^{''}} + y = sin (2) (x)

What is the derivative of f(x)=(1+7x^2)(x-x^2) ?
The derivative of f(x)=(1+7x^2)(x-x^2) is -28x^3+21x^2-2x+1
What is the first derivative of f(x)=(1+7x^2)(x-x^2) ?
The first derivative of f(x)=(1+7x^2)(x-x^2) is -28x^3+21x^2-2x+1