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

The derivative of (e^x^{sin(x)}) is e^{xsin(x)}(sin(x)+xcos(x))

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

The first derivative of (e^x^{sin(x)}) is e^{xsin(x)}(sin(x)+xcos(x))

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

y = x^{3} - 7 x^{2} + 16 x + 7

(0, - 2), (5, - 4)

\int_{0}^{3} 2 e^{- 3 x} d x

\int x^{3} sin (x^{2}) d x

\frac{\partial}{\partial x} (cos^{9} (x^{4} y^{8}))

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