What is the derivative of e^{sin(x}) ?

The derivative of e^{sin(x}) is e^{sin(x)}cos(x)

What is the first derivative of e^{sin(x}) ?

The first derivative of e^{sin(x}) is e^{sin(x)}cos(x)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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