What is (\partial)/(\partial x)(e^{5x}cos(7y)) ?

The answer to (\partial)/(\partial x)(e^{5x}cos(7y)) is cos(7y)e^{5x}*5

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(\partial)/(\partial x)(e^{5x}cos(7y))

\frac{\partial}{\partial x} (e^{5 x} cos (7 y))

cos (7 y) e^{5 x} \cdot 5

Solution steps

\frac{\partial}{\partial x} (e^{5 x} cos (7 y))

Treat

y

as a constant

Take the constant out:

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

= cos (7 y) \frac{\partial}{\partial x} (e^{5 x})

Apply the chain rule:

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

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

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

= cos (7 y) e^{5 x} \cdot 5

What is (\partial)/(\partial x)(e^{5x}cos(7y)) ?
The answer to (\partial)/(\partial x)(e^{5x}cos(7y)) is cos(7y)e^{5x}*5