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

The answer to (\partial)/(\partial x)(5e^{7x}sin(7y)) is 35e^{7x}sin(7y)

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

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

35 e^{7 x} sin (7 y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

e^{7 x} \frac{\partial}{\partial x} (7 x)

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

\frac{\partial}{\partial x} (7 x) = 7

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

Simplify

= 35 e^{7 x} sin (7 y)

\int (x^{6} - \frac{1}{x ^{6}})^{2} d x

\int e^{\frac{x}{9}} d x

θ \to 0 lim (\frac{cos ( θ ) - 1}{sin ( θ )})

y = x^{3} + x^{2}, y = 6 x

f (t) = 2 t^{4}

What is (\partial)/(\partial x)(5e^{7x}sin(7y)) ?
The answer to (\partial)/(\partial x)(5e^{7x}sin(7y)) is 35e^{7x}sin(7y)