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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

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

\int \frac{1}{( 3 + 2 x ) ^{2}} d x

\int_{0}^{2} 4 t i - t^{3} j + 4 t^{7} k d t

\frac{d}{d x} (- \frac{x}{x - 1})

x \to 0 lim (\frac{9 cos ( x ) - 9}{x})

\frac{d}{d x} (\frac{x - 6}{3 x - 2})

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