What is (\partial)/(\partial x)(e^xcos(2x)) ?

The answer to (\partial)/(\partial x)(e^xcos(2x)) is e^xcos(2x)-2e^xsin(2x)

Popular >

(\partial)/(\partial x)(e^xcos(2x))

\frac{\partial}{\partial x} (e^{x} cos (2 x))

e^{x} cos (2 x) - 2 e^{x} sin (2 x)

Solution steps

\frac{\partial}{\partial x} (e^{x} cos (2 x))

Apply the Product Rule:

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

f = e^{x}, g = cos (2 x)

= \frac{\partial}{\partial x} (e^{x}) cos (2 x) + \frac{\partial}{\partial x} (cos (2 x)) e^{x}

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

\frac{\partial}{\partial x} (cos (2 x)) = - sin (2 x) \cdot 2

= e^{x} cos (2 x) + (- sin (2 x) \cdot 2) e^{x}

Simplify

= e^{x} cos (2 x) - 2 e^{x} sin (2 x)

\frac{s ^{2} + 4}{( s ^{2} - 4 ) ^{2}}

5 x - 8 y x^{2} + 1 \frac{d y}{d x} = 0

2 ln (\frac{3 x ^{2}}{2})

\frac{d}{d x} ((4 x^{2} + 9) (8 x + x^{\frac{1}{2}}))

y = 7 x^{\frac{1}{2}} + x^{\frac{3}{2}}

What is (\partial)/(\partial x)(e^xcos(2x)) ?
The answer to (\partial)/(\partial x)(e^xcos(2x)) is e^xcos(2x)-2e^xsin(2x)