What is (\partial)/(\partial x)(sin(z^2)cos(xy)) ?

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

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(\partial)/(\partial x)(sin(z^2)cos(xy))

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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