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

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

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(\partial)/(\partial y)(cos(x^2y))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

\int (sec (t) - 1)^{2} d t

tan (5 x + y) = 5 x

y = x^{3}, [0, 4]

f (x) = \frac{x ^{2}}{( 2 + x )}

\int (x - 1)^{- 3} d x

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