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

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

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

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

cos (x^{2}) cos (yz) z

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

cos (yz) \frac{\partial}{\partial y} (yz)

= cos (yz) \frac{\partial}{\partial y} (yz)

\frac{\partial}{\partial y} (yz) = z

= cos (x^{2}) cos (yz) z

\frac{d y}{d x} = \frac{y ^{2} + 4 x x ^{2} + y ^{2}}{x y}

f (x) = \frac{1}{x ^{5}}

f (x) = (x^{3} - 3 x) (2 x^{2} + 3 x + 5)

\int 2 sin (θ) - sec^{2} (θ) d θ

x \to + 0 lim (\frac{x}{arctan ( x )})

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