What is (\partial)/(\partial x)((z)(xy^5-x^2y)) ?

The answer to (\partial)/(\partial x)((z)(xy^5-x^2y)) is z(y^5-2yx)

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(\partial)/(\partial x)((z)(xy^5-x^2y))

\frac{\partial}{\partial x} ((z) (x y^{5} - x^{2} y))

z (y^{5} - 2 y x)

Solution steps

\frac{\partial}{\partial x} ((z) (x y^{5} - x^{2} y))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (x y^{5} - x^{2} y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{\partial}{\partial x} (x y^{5}) - \frac{\partial}{\partial x} (x^{2} y))

\frac{\partial}{\partial x} (x y^{5}) = y^{5}

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

= z (y^{5} - 2 y x)

\frac{tan ^{2} ( x )}{( sec ( x ) - 1 ) ^{2}}

(x - 23)^{2}

\frac{- x ^{2} - 2 x + 3}{( x ^{2} + 3 ) ^{2}}

(2 x^{3} - \frac{1}{x})^{12}

(t cos (t)) (cos (t) - t sin (t))

What is (\partial)/(\partial x)((z)(xy^5-x^2y)) ?
The answer to (\partial)/(\partial x)((z)(xy^5-x^2y)) is z(y^5-2yx)