What is the derivative of 4x^2+1/(x^2+3x^4) ?

The derivative of 4x^2+1/(x^2+3x^4) is 8x-2/(x^3)+12x^3

What is the first derivative of 4x^2+1/(x^2+3x^4) ?

The first derivative of 4x^2+1/(x^2+3x^4) is 8x-2/(x^3)+12x^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (4 x^{2} + \frac{1}{x ^{2}} + 3 x^{4})

8 x - \frac{2}{x ^{3}} + 12 x^{3}

Solution steps

\frac{d}{d x} (4 x^{2} + \frac{1}{x ^{2}} + 3 x^{4})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{2}) + \frac{d}{d x} (\frac{1}{x ^{2}}) + \frac{d}{d x} (3 x^{4})

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

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

= 8 x - \frac{2}{x ^{3}} + 12 x^{3}

What is the derivative of 4x^2+1/(x^2+3x^4) ?
The derivative of 4x^2+1/(x^2+3x^4) is 8x-2/(x^3)+12x^3
What is the first derivative of 4x^2+1/(x^2+3x^4) ?
The first derivative of 4x^2+1/(x^2+3x^4) is 8x-2/(x^3)+12x^3