en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (e^x/(sin(x)))

Solution

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

Solution

e^{x} csc (x) - e^{x} cot (x) csc (x)

Solution steps

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

Simplify

\frac{e ^{x}}{sin ( x )} : e^{x} csc (x)

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

Apply the Product Rule:

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

f = e^{x}, g = csc (x)

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

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= e^{x} csc (x) + (- cot (x) csc (x)) e^{x}

Simplify

= e^{x} csc (x) - e^{x} cot (x) csc (x)

Graph

Popular Examples

derivative of sec^2(x)-tan^2(x)

d er i v a t i v e sec^{2} (x) - tan^{2} (x)

derivative of sin(x+1/(sqrt(x)))

\frac{d}{d x} (sin (x) + \frac{1}{x})

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

n = 2 \sum \infty \frac{1}{n ^{n}}

sum from n=0 to infinity of (1+1/n)^n

n = 0 \sum \infty (1 + \frac{1}{n})^{n}

derivative of \sqrt[3]{sec(5x})

\frac{d}{d x} (3 sec (5 x))

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(sin(x))) ?
The derivative of (e^x/(sin(x))) is e^xcsc(x)-e^xcot(x)csc(x)
What is the first derivative of (e^x/(sin(x))) ?
The first derivative of (e^x/(sin(x))) is e^xcsc(x)-e^xcot(x)csc(x)