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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= sin (5 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

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

\frac{x ^{2} - 1}{x ^{2} + x + 1}

y = - \frac{2}{x ^{2}}

2 sin (4 π (x + \frac{1}{8}))

\int \frac{x + 1}{x - 1} d x

x \to - 1 lim (8 x^{3})

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