en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(e^{sin(x)})

Solution

\frac{d}{d x} (e^{s i n (x)})

Solution

\frac{e ^{s i n (x)} cos ( x )}{2 e ^{s i n (x)}}

Solution steps

\frac{d}{d x} (e^{s i n (x)})

Apply the chain rule:

\frac{1}{2 e ^{s i n (x)}} \frac{d}{d x} (e^{s i n (x)})

= \frac{1}{2 e ^{s i n (x)}} \frac{d}{d x} (e^{s i n (x)})

\frac{d}{d x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

= \frac{1}{2 e ^{s i n (x)}} e^{s i n (x)} cos (x)

Simplify

\frac{1}{2 e ^{s i n (x)}} e^{s i n (x)} cos (x) : \frac{e ^{s i n (x)} cos ( x )}{2 e ^{s i n (x)}}

= \frac{e ^{s i n (x)} cos ( x )}{2 e ^{s i n (x)}}

Graph

Popular Examples

limit as x approaches 2 of (x-2)/((x-2))

x \to 2 lim (\frac{x - 2}{( x - 2 )})

tangent of y=x+sin(x)tangent of

y = x + sin (x)

derivative of (2x^3-12x^{4/3})

\frac{d}{d x} ((2 x^{3} - 12 x)^{\frac{4}{3}})

(\partial)/(\partial x)(x/(x^2+4y^2))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 4 y ^{2}})

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

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

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(e^{sin(x)}) ?
The derivative of sqrt(e^{sin(x)}) is (e^{sin(x)}cos(x))/(2sqrt(e^{sin(x)))}
What is the first derivative of sqrt(e^{sin(x)}) ?
The first derivative of sqrt(e^{sin(x)}) is (e^{sin(x)}cos(x))/(2sqrt(e^{sin(x)))}