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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

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