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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

- \frac{12}{x ^{6}}

cos (4 x^{2})

\int \frac{( x + 9 )}{x} d x

\int \frac{1}{3 - 3 x} d x

x y y^{^{'}} = 1 + y^{2}

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