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

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

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

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

- cos (x^{2} - y)

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x^{2} - y) = - 1

= cos (x^{2} - y) (- 1)

Simplify

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

\int (tan^{3} (x)) d x

y = x^{2}, y = x + 2, 0

y = \frac{x}{x ^{2} - 4 x + 5}, y = \frac{3}{x ^{2} - 4 x + 5}, x = 0

y = \frac{x ^{3} + 1}{6 x}, x = 1

y^{^{'}} + 4 y = e^{- x}, y (0) = 10

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