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

The answer to (\partial)/(\partial x)(sin(x^2-y)) is cos(x^2-y)*2x

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

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

cos (x^{2} - y) \cdot 2 x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (x^{2} - y) \cdot 2 x

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\frac{d}{d x} (12 + 5 sin (π x))

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