What is (\partial)/(\partial y)(e^{3x+4y}cos(5z)) ?

The answer to (\partial)/(\partial y)(e^{3x+4y}cos(5z)) is cos(5z)e^{3x+4y}*4

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(\partial)/(\partial y)(e^{3x+4y}cos(5z))

\frac{\partial}{\partial y} (e^{3 x + 4 y} cos (5 z))

cos (5 z) e^{3 x + 4 y} \cdot 4

Solution steps

\frac{\partial}{\partial y} (e^{3 x + 4 y} cos (5 z))

Treat

x, z

as constants

Take the constant out:

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

= cos (5 z) \frac{\partial}{\partial y} (e^{3 x + 4 y})

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (3 x + 4 y) = 4

= cos (5 z) e^{3 x + 4 y} \cdot 4

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What is (\partial)/(\partial y)(e^{3x+4y}cos(5z)) ?
The answer to (\partial)/(\partial y)(e^{3x+4y}cos(5z)) is cos(5z)e^{3x+4y}*4