What is (\partial)/(\partial x)(e^xcos(x)) ?

The answer to (\partial)/(\partial x)(e^xcos(x)) is e^xcos(x)-e^xsin(x)

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(\partial)/(\partial x)(e^xcos(x))

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (x)

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

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

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

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

Simplify

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

f (x) = x^{2} + 5

\frac{d}{d x} (cos (2 x + π))

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

(9 - 2 x^{3})^{3}

\frac{d}{d x} (x^{r})

What is (\partial)/(\partial x)(e^xcos(x)) ?
The answer to (\partial)/(\partial x)(e^xcos(x)) is e^xcos(x)-e^xsin(x)