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

The answer to (\partial)/(\partial x)(e^{6y}sin(-6x)) is -e^{6y}cos(6x)*6

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

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

- e^{6 y} cos (6 x) \cdot 6

Solution steps

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

Simplify

e^{6 y} sin (- 6 x) : - e^{6 y} sin (6 x)

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - e^{6 y} cos (6 x) \cdot 6

n = 1 \sum \infty 17 - \frac{7}{n ^{3}}

\int sinh (x) cosh^{4} (x) d x

y = 2 x^{2}, y = 3 - x

x \to 5 lim (\frac{4 x}{x - 5})

What is (\partial)/(\partial x)(e^{6y}sin(-6x)) ?
The answer to (\partial)/(\partial x)(e^{6y}sin(-6x)) is -e^{6y}cos(6x)*6