What is (\partial)/(\partial x)(e^{3x}cos(4x)) ?

The answer to (\partial)/(\partial x)(e^{3x}cos(4x)) is 3e^{3x}cos(4x)-4e^{3x}sin(4x)

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(\partial)/(\partial x)(e^{3x}cos(4x))

\frac{\partial}{\partial x} (e^{3 x} cos (4 x))

3 e^{3 x} cos (4 x) - 4 e^{3 x} sin (4 x)

Solution steps

\frac{\partial}{\partial x} (e^{3 x} cos (4 x))

Apply the Product Rule:

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

f = e^{3 x}, g = cos (4 x)

= \frac{\partial}{\partial x} (e^{3 x}) cos (4 x) + \frac{\partial}{\partial x} (cos (4 x)) e^{3 x}

\frac{\partial}{\partial x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{\partial}{\partial x} (cos (4 x)) = - sin (4 x) \cdot 4

= e^{3 x} \cdot 3 cos (4 x) + (- sin (4 x) \cdot 4) e^{3 x}

Simplify

= 3 e^{3 x} cos (4 x) - 4 e^{3 x} sin (4 x)

\frac{d}{d t} (3 + 3 cos (t^{3}) - 4 sin (t^{3}))

x^{- 10}

y^{^{'}} + 5 y = 2 e^{(6 \cdot x)}

\frac{\partial}{\partial z} (x^{2} yz - x y z^{3})

\frac{y ^{4}}{8}

What is (\partial)/(\partial x)(e^{3x}cos(4x)) ?
The answer to (\partial)/(\partial x)(e^{3x}cos(4x)) is 3e^{3x}cos(4x)-4e^{3x}sin(4x)