What is (\partial)/(\partial y)(e^{3x}cos(8y)) ?

The answer to (\partial)/(\partial y)(e^{3x}cos(8y)) is -8e^{3x}sin(8y)

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(\partial)/(\partial y)(e^{3x}cos(8y))

\frac{\partial}{\partial y} (e^{3 x} cos (8 y))

- 8 e^{3 x} sin (8 y)

Solution steps

\frac{\partial}{\partial y} (e^{3 x} cos (8 y))

Treat

x

as a constant

Take the constant out:

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

= e^{3 x} \frac{\partial}{\partial y} (cos (8 y))

Apply the chain rule:

- sin (8 y) \frac{\partial}{\partial y} (8 y)

= - sin (8 y) \frac{\partial}{\partial y} (8 y)

\frac{\partial}{\partial y} (8 y) = 8

= e^{3 x} (- sin (8 y) \cdot 8)

Simplify

= - 8 e^{3 x} sin (8 y)

\int e^{- t} d t

\int \frac{1 + cos ( x )}{sin ( x )} d x

x \to 2 lim (\frac{3}{x + 1})

\int (2 x - 5)^{- \frac{1}{2}} d x

\frac{\partial}{\partial x} (y x^{3})

What is (\partial)/(\partial y)(e^{3x}cos(8y)) ?
The answer to (\partial)/(\partial y)(e^{3x}cos(8y)) is -8e^{3x}sin(8y)