en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^x+ln(x-1/x)

Solution

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

Solution

e^{x} + \frac{1}{x} + \frac{1}{x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{x}) + \frac{d}{d x} (ln (x)) - \frac{d}{d x} (\frac{1}{x})

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

Simplify

= e^{x} + \frac{1}{x} + \frac{1}{x ^{2}}

Popular Examples

sum from n=1 to infinity of 1/((2n+3)^3)

n = 1 \sum \infty \frac{1}{( 2 n + 3 ) ^{3}}

tangent of f(x)=8(x-1/x),\at x=2 tangent of

f (x) = 8 (x - \frac{1}{x}), at x = 2

derivative of f(x^2(x))

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

\frac{d}{d t} (t^{3} e^{t})

derivative of (ln(x-1)^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of e^x+ln(x-1/x) ?
The derivative of e^x+ln(x-1/x) is e^x+1/x+1/(x^2)
What is the first derivative of e^x+ln(x-1/x) ?
The first derivative of e^x+ln(x-1/x) is e^x+1/x+1/(x^2)