What is the derivative of e^{xsin(3x}) ?

The derivative of e^{xsin(3x}) is e^{xsin(3x)}(sin(3x)+3xcos(3x))

What is the first derivative of e^{xsin(3x}) ?

The first derivative of e^{xsin(3x}) is e^{xsin(3x)}(sin(3x)+3xcos(3x))

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\frac{d}{d x} (e^{x s i n (3 x)})

e^{x s i n (3 x)} (sin (3 x) + 3 x cos (3 x))

Solution steps

\frac{d}{d x} (e^{x s i n (3 x)})

Apply the chain rule:

e^{x s i n (3 x)} \frac{d}{d x} (x sin (3 x))

= e^{x s i n (3 x)} \frac{d}{d x} (x sin (3 x))

\frac{d}{d x} (x sin (3 x)) = sin (3 x) + 3 x cos (3 x)

= e^{x s i n (3 x)} (sin (3 x) + 3 x cos (3 x))

\int_{0}^{5} \frac{2 t}{( t - 6 ) ^{2}} d t

\int \frac{x + 2}{x ^{2} + 6 x + 10} d x

x y^{^{'}} + 3 y = \frac{( e ^{x} )}{x}

\frac{\partial}{\partial y} (5 x sin (y))

in v erse l a pl a ce 3 x^{2}

What is the derivative of e^{xsin(3x}) ?
The derivative of e^{xsin(3x}) is e^{xsin(3x)}(sin(3x)+3xcos(3x))
What is the first derivative of e^{xsin(3x}) ?
The first derivative of e^{xsin(3x}) is e^{xsin(3x)}(sin(3x)+3xcos(3x))