What is (\partial)/(\partial x)((cos(x^2*y))/(z^3)) ?

The answer to (\partial)/(\partial x)((cos(x^2*y))/(z^3)) is -(2xysin(x^2y))/(z^3)

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(\partial)/(\partial x)((cos(x^2*y))/(z^3))

\frac{\partial}{\partial x} (\frac{cos ( x ^{2} \cdot y )}{z ^{3}})

- \frac{2 x y sin ( x ^{2} y )}{z ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{cos ( x ^{2} y )}{z ^{3}})

Treat

y, z

as constants

Take the constant out:

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

= \frac{1}{z ^{3}} \frac{\partial}{\partial x} (cos (x^{2} y))

Apply the chain rule:

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

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

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

= \frac{1}{z ^{3}} (- sin (x^{2} y) \cdot 2 y x)

Simplify

\frac{1}{z ^{3}} (- sin (x^{2} y) \cdot 2 y x) : - \frac{2 x y sin ( x ^{2} y )}{z ^{3}}

= - \frac{2 x y sin ( x ^{2} y )}{z ^{3}}

im pl i c i t \frac{d y}{d x}, 5 x y^{5} + 3 x y = 24

d er i v a t i v e arctan (\frac{x}{6})

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

\frac{d}{d x} (ln (\frac{1}{6 + x}))

x \to 3 lim (x + 1)

What is (\partial)/(\partial x)((cos(x^2*y))/(z^3)) ?
The answer to (\partial)/(\partial x)((cos(x^2*y))/(z^3)) is -(2xysin(x^2y))/(z^3)