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Popular Calculus >

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 )})

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

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

64y^{''}+80y^'+25y=0,y(0)=a,y^'(0)=-5

64 y^{^{''}} + 80 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 5

integral of 7arcsin(x)

\int 7 arcsin (x) d x

limit as z approaches 10 of 1/(z-10)

z \to 10 lim (\frac{1}{z - 10})

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)))}