en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 5x^3+x^2+1/x

Solution

\frac{d}{d x} (5 x^{3} + x^{2} + \frac{1}{x})

Solution

15 x^{2} + 2 x - \frac{1}{x ^{2}}

Solution steps

\frac{d}{d x} (5 x^{3} + x^{2} + \frac{1}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x^{3}) + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

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

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

= 15 x^{2} + 2 x - \frac{1}{x ^{2}}

Popular Examples

derivative of 2(5-9x^5)

\frac{d}{d x} (2 (5 - 9 x)^{5})

integral of (1-x)/(1-x^2)

\int \frac{1 - x}{1 - x ^{2}} d x

integral from 0 to 2 of (x^2-2x)

\int_{0}^{2} (x^{2} - 2 x) d x

integral of sin^2(x+4)

\int sin^{2} (x + 4) d x

integral from 1 to infinity of xe^{-4x}

\int_{1}^{\infty} x e^{- 4 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 5x^3+x^2+1/x ?
The derivative of 5x^3+x^2+1/x is 15x^2+2x-1/(x^2)
What is the first derivative of 5x^3+x^2+1/x ?
The first derivative of 5x^3+x^2+1/x is 15x^2+2x-1/(x^2)