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Popular >

derivative of e^xsin(x+e^xcos(x))

Solution

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

Solution

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)

Popular Examples

integral of (x^3)/((1-x^4)^6)

\int \frac{x ^{3}}{( 1 - x ^{4} ) ^{6}} d x

derivative of x^2e^x-2xe^x+8e^x

\frac{d}{d x} (x^{2} e^{x} - 2 x e^{x} + 8 e^{x})

(\partial)/(\partial x)(1-xy)

\frac{\partial}{\partial x} (1 - x y)

limit as x approaches 0 of (6^x-1)/x

x \to 0 lim (\frac{6 ^{x} - 1}{x})

derivative of e^{x-7}

\frac{d}{d x} (e^{x - 7})

Frequently Asked Questions (FAQ)

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)