What is (\partial)/(\partial x)(e^{2y}cos(3x)) ?

The answer to (\partial)/(\partial x)(e^{2y}cos(3x)) is -3e^{2y}sin(3x)

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(\partial)/(\partial x)(e^{2y}cos(3x))

\frac{\partial}{\partial x} (e^{2 y} cos (3 x))

- 3 e^{2 y} sin (3 x)

Solution steps

\frac{\partial}{\partial x} (e^{2 y} cos (3 x))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= e^{2 y} \frac{\partial}{\partial x} (cos (3 x))

Apply the chain rule:

- sin (3 x) \frac{\partial}{\partial x} (3 x)

= - sin (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= e^{2 y} (- sin (3 x) \cdot 3)

Simplify

= - 3 e^{2 y} sin (3 x)

3

y^{^{''}} - 5 y^{^{'}} + 6 y = x \cdot e^{(- 4 \cdot x)}

\frac{d}{d x} (\frac{5}{( 2 x ) ^{3}})

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

\int (tan (\frac{x}{10}))^{5} d x

What is (\partial)/(\partial x)(e^{2y}cos(3x)) ?
The answer to (\partial)/(\partial x)(e^{2y}cos(3x)) is -3e^{2y}sin(3x)