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

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

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

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

- sin (x - y^{2})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= - sin (x - y^{2}) \cdot 1

Simplify

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

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