What is the derivative of e^{xsin(2x}) ?

The derivative of e^{xsin(2x}) is e^{xsin(2x)}(sin(2x)+2xcos(2x))

What is the first derivative of e^{xsin(2x}) ?

The first derivative of e^{xsin(2x}) is e^{xsin(2x)}(sin(2x)+2xcos(2x))

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\frac{d}{d x} (e^{x s i n (2 x)})

e^{x s i n (2 x)} (sin (2 x) + 2 x cos (2 x))

Solution steps

\frac{d}{d x} (e^{x s i n (2 x)})

Apply the chain rule:

e^{x s i n (2 x)} \frac{d}{d x} (x sin (2 x))

= e^{x s i n (2 x)} \frac{d}{d x} (x sin (2 x))

\frac{d}{d x} (x sin (2 x)) = sin (2 x) + 2 x cos (2 x)

= e^{x s i n (2 x)} (sin (2 x) + 2 x cos (2 x))

x \to 0 lim (x^{7} e^{- x^{6}})

\frac{1 + s}{s ^{3} - 2 s ^{2}}

\frac{\partial}{\partial x} (21 y^{3} cos (7 y^{2} x))

\frac{d}{d x} (sin^{2} (π x))

\frac{d y}{d x} = \frac{2 sec ( y )}{( x - 2 ) ^{2}}

What is the derivative of e^{xsin(2x}) ?
The derivative of e^{xsin(2x}) is e^{xsin(2x)}(sin(2x)+2xcos(2x))
What is the first derivative of e^{xsin(2x}) ?
The first derivative of e^{xsin(2x}) is e^{xsin(2x)}(sin(2x)+2xcos(2x))