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

The derivative of e^xsin(xcos(x)) is e^xsin(x)cos(x)+cos(2x)e^x

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

The first derivative of e^xsin(xcos(x)) is e^xsin(x)cos(x)+cos(2x)e^x

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\frac{d}{d x} (e^{x} sin (x) cos (x))

e^{x} sin (x) cos (x) + cos (2 x) e^{x}

Solution steps

\frac{d}{d x} (e^{x} sin (x) cos (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = sin (x) cos (x)

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

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

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

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

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