What is (\partial)/(\partial x)(e^{ysin(x)}) ?

The answer to (\partial)/(\partial x)(e^{ysin(x)}) is e^{ysin(x)}ycos(x)

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(\partial)/(\partial x)(e^{ysin(x)})

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

e^{y s i n (x)} y cos (x)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

e^{y s i n (x)} \frac{\partial}{\partial x} (y sin (x))

= e^{y s i n (x)} \frac{\partial}{\partial x} (y sin (x))

\frac{\partial}{\partial x} (y sin (x)) = y cos (x)

= e^{y s i n (x)} y cos (x)

\frac{d}{d x} (4 9 - x)

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

\frac{d}{d x} (\frac{5 x ^{2} + 2 x - 6}{3 x - 1})

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

\frac{d}{d x} (ln (x) sin (x) cos (x))

What is (\partial)/(\partial x)(e^{ysin(x)}) ?
The answer to (\partial)/(\partial x)(e^{ysin(x)}) is e^{ysin(x)}ycos(x)