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

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

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

The first derivative of e^{xsin(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)})

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))

\int (x^{2} x^{3} + 1) d x

\frac{d y}{d t} = 0.225 - 0.0045 y

\int sin^{5} (8 θ) d θ

\frac{d}{d x} (arcsec (e^{x}))

(2) (1)

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