What is (\partial)/(\partial x)(-x-x^3sin(2y)) ?

The answer to (\partial)/(\partial x)(-x-x^3sin(2y)) is -1-3x^2sin(2y)

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(\partial)/(\partial x)(-x-x^3sin(2y))

\frac{\partial}{\partial x} (- x - x^{3} sin (2 y))

- 1 - 3 x^{2} sin (2 y)

Solution steps

\frac{\partial}{\partial x} (- x - x^{3} sin (2 y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (x^{3} sin (2 y))

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x^{3} sin (2 y)) = 3 x^{2} sin (2 y)

= - 1 - 3 x^{2} sin (2 y)

What is (\partial)/(\partial x)(-x-x^3sin(2y)) ?
The answer to (\partial)/(\partial x)(-x-x^3sin(2y)) is -1-3x^2sin(2y)