What is (\partial)/(\partial x)(\sqrt[3]{(y-5x)^2}) ?

The answer to (\partial)/(\partial x)(\sqrt[3]{(y-5x)^2}) is -(10)/(3(y-5x)^{1/3)}

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(\partial)/(\partial x)(\sqrt[3]{(y-5x)^2})

- \frac{10}{3 ( y - 5 x ) ^{\frac{1}{3}}}

Solution steps

Treat

y

as a constant

Apply the chain rule:

\frac{1}{3 ( ( y - 5 x ) ^{2} ) ^{\frac{2}{3}}} \frac{\partial}{\partial x} ((y - 5 x)^{2})

= \frac{1}{3 ( ( y - 5 x ) ^{2} ) ^{\frac{2}{3}}} \frac{\partial}{\partial x} ((y - 5 x)^{2})

\frac{\partial}{\partial x} ((y - 5 x)^{2}) = - 10 (y - 5 x)

= \frac{1}{3 ( ( y - 5 x ) ^{2} ) ^{\frac{2}{3}}} (- 10 (y - 5 x))

Simplify

\frac{1}{3 ( ( y - 5 x ) ^{2} ) ^{\frac{2}{3}}} (- 10 (y - 5 x)) : - \frac{10}{3 ( y - 5 x ) ^{\frac{1}{3}}}

= - \frac{10}{3 ( y - 5 x ) ^{\frac{1}{3}}}

x \to 2 lim (\frac{x ^{2} - 9}{x + 2})

\frac{\partial}{\partial x} (e^{x y})

\frac{d}{d x} (\frac{4}{( x + 4 ) ^{2}})

t \cdot \frac{d y}{d t} = t^{3} + 22 t^{3} y

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

What is (\partial)/(\partial x)(\sqrt[3]{(y-5x)^2}) ?
The answer to (\partial)/(\partial x)(\sqrt[3]{(y-5x)^2}) is -(10)/(3(y-5x)^{1/3)}