What is (\partial)/(\partial x)(sin(7y^2-7xy)) ?

The answer to (\partial)/(\partial x)(sin(7y^2-7xy)) is -7ycos(7y^2-7yx)

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(\partial)/(\partial x)(sin(7y^2-7xy))

\frac{\partial}{\partial x} (sin (7 y^{2} - 7 x y))

- 7 y cos (7 y^{2} - 7 y x)

Solution steps

\frac{\partial}{\partial x} (sin (7 y^{2} - 7 x y))

Treat

y

as a constant

Apply the chain rule:

cos (7 y^{2} - 7 x y) \frac{\partial}{\partial x} (7 y^{2} - 7 x y)

= cos (7 y^{2} - 7 x y) \frac{\partial}{\partial x} (7 y^{2} - 7 x y)

\frac{\partial}{\partial x} (7 y^{2} - 7 x y) = - 7 y

= cos (7 y^{2} - 7 x y) (- 7 y)

Simplify

= - 7 y cos (7 y^{2} - 7 y x)

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What is (\partial)/(\partial x)(sin(7y^2-7xy)) ?
The answer to (\partial)/(\partial x)(sin(7y^2-7xy)) is -7ycos(7y^2-7yx)