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

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

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

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

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

2 e^{x} cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= 2 e^{x} cos (x)

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

\int \frac{1}{( 169 - x ^{2} ) ^{\frac{3}{2}}} d x

1 - x^{3}

6 x^{2}, x^{2} + 5

\int - \frac{1}{u} d u

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