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

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

Popular >

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

y = \frac{5}{4 x + 1}

\frac{d}{d x} (\frac{3 - 17 x ^{2}}{3 x ^{3}})

5 e^{x} tan (x)

\int \frac{4 x ^{2} + 3 x - 1}{x ^{3} - x ^{2}} d x

\frac{\partial}{\partial y} (\frac{y}{x + z})

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