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

The derivative of e^xsin(x+cos(x)) is e^xsin(x)+cos(x)e^x-sin(x)

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

The first derivative of e^xsin(x+cos(x)) is e^xsin(x)+cos(x)e^x-sin(x)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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