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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

\int a^{u} d u

\frac{3}{t ^{2}}

\int cos^{3} (θ) d θ

\frac{\partial}{\partial x} (\frac{( x + y )}{x - y})

\int_{0}^{1} 1 + x^{4} + 2 x^{2} d x

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