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

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

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

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

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derivative of

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

2 e^{x} cos (x)

Solution steps

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

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

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

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

Simplify

= 2 e^{x} cos (x)

f (x) = \frac{1}{4 - x ^{2}}

\int_{1}^{4} 3 x - 6 d x

\int_{1}^{2} x (x - 1) d x

\frac{\partial}{\partial y} (y e^{x})

\int 24 x (6 x^{2} - 1)^{5} d x

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