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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

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