What is (\partial)/(\partial x)(7e^{6x}sin(5y)) ?

The answer to (\partial)/(\partial x)(7e^{6x}sin(5y)) is 42e^{6x}sin(5y)

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(\partial)/(\partial x)(7e^{6x}sin(5y))

\frac{\partial}{\partial x} (7 e^{6 x} sin (5 y))

42 e^{6 x} sin (5 y)

Solution steps

\frac{\partial}{\partial x} (7 e^{6 x} sin (5 y))

Treat

y

as a constant

Take the constant out:

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

= 7 sin (5 y) \frac{\partial}{\partial x} (e^{6 x})

Apply the chain rule:

e^{6 x} \frac{\partial}{\partial x} (6 x)

= e^{6 x} \frac{\partial}{\partial x} (6 x)

\frac{\partial}{\partial x} (6 x) = 6

= 7 sin (5 y) e^{6 x} \cdot 6

Simplify

= 42 e^{6 x} sin (5 y)

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What is (\partial)/(\partial x)(7e^{6x}sin(5y)) ?
The answer to (\partial)/(\partial x)(7e^{6x}sin(5y)) is 42e^{6x}sin(5y)