What is (\partial)/(\partial y)(e^{5y}cos(-5x)) ?

The answer to (\partial)/(\partial y)(e^{5y}cos(-5x)) is cos(5x)e^{5y}*5

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(\partial)/(\partial y)(e^{5y}cos(-5x))

\frac{\partial}{\partial y} (e^{5 y} cos (- 5 x))

cos (5 x) e^{5 y} \cdot 5

Solution steps

\frac{\partial}{\partial y} (e^{5 y} cos (- 5 x))

Simplify

e^{5 y} cos (- 5 x) : e^{5 y} cos (5 x)

= \frac{\partial}{\partial y} (e^{5 y} cos (5 x))

Treat

x

as a constant

Take the constant out:

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

= cos (5 x) \frac{\partial}{\partial y} (e^{5 y})

Apply the chain rule:

e^{5 y} \frac{\partial}{\partial y} (5 y)

= e^{5 y} \frac{\partial}{\partial y} (5 y)

\frac{\partial}{\partial y} (5 y) = 5

= cos (5 x) e^{5 y} \cdot 5

\int e^{x} sin (4 x) d x

\frac{d}{d x} (lo g_{3} (4 x + 1))

\frac{\partial}{\partial y} (- 9 sin (3 x + yz))

x \to \frac{π}{8} lim (tan (24 x))

tan (8 x)

What is (\partial)/(\partial y)(e^{5y}cos(-5x)) ?
The answer to (\partial)/(\partial y)(e^{5y}cos(-5x)) is cos(5x)e^{5y}*5