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

The answer to (\partial)/(\partial x)(e^{cos(x)}) is -e^{cos(x)}sin(x)

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

\frac{\partial}{\partial x} (e^{c o s (x)})

- e^{c o s (x)} sin (x)

Solution steps

\frac{\partial}{\partial x} (e^{c o s (x)})

Apply the chain rule:

e^{c o s (x)} \frac{\partial}{\partial x} (cos (x))

= e^{c o s (x)} \frac{\partial}{\partial x} (cos (x))

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

= e^{c o s (x)} (- sin (x))

Simplify

= - e^{c o s (x)} sin (x)

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What is (\partial)/(\partial x)(e^{cos(x)}) ?
The answer to (\partial)/(\partial x)(e^{cos(x)}) is -e^{cos(x)}sin(x)