What is the derivative of x^7+1/(x^7+7x+7/x+7) ?

The derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7

What is the first derivative of x^7+1/(x^7+7x+7/x+7) ?

The first derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

7 x^{6} - \frac{7}{x ^{8}} - \frac{7}{x ^{2}} + 7

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (\frac{1}{x ^{7}}) = - \frac{7}{x ^{8}}

\frac{d}{d x} (7 x) = 7

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

\frac{d}{d x} (7) = 0

= 7 x^{6} - \frac{7}{x ^{8}} + 7 - \frac{7}{x ^{2}} + 0

Simplify

= 7 x^{6} - \frac{7}{x ^{8}} - \frac{7}{x ^{2}} + 7

\frac{\partial}{\partial x} (b x)

\frac{d y}{d t} - 2 y = e^{2 t}

\frac{\partial}{\partial x} (x z ln (x + y + z))

\frac{4 d y}{d x} = y^{2}

arctan (x)

What is the derivative of x^7+1/(x^7+7x+7/x+7) ?
The derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7
What is the first derivative of x^7+1/(x^7+7x+7/x+7) ?
The first derivative of x^7+1/(x^7+7x+7/x+7) is 7x^6-7/(x^8)-7/(x^2)+7