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

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

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

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

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derivative of

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

2 e^{x} cos (x)

Solution steps

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

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

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

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

Simplify

= 2 e^{x} cos (x)

\int y y^{2} + 1 d y

x \to 3 lim (2 x + 4)

n = 0 \sum \infty 2 \cdot 0. 3^{n}

\frac{d y}{d x} + x (y^{2} + y) = 0

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