What is (\partial)/(\partial x)((x-1)^{2/3}(y^2-4)) ?

The answer to (\partial)/(\partial x)((x-1)^{2/3}(y^2-4)) is (2(y^2-4))/(3(x-1)^{1/3)}

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(\partial)/(\partial x)((x-1)^{2/3}(y^2-4))

\frac{\partial}{\partial x} ((x - 1)^{\frac{2}{3}} (y^{2} - 4))

\frac{2 ( y ^{2} - 4 )}{3 ( x - 1 ) ^{\frac{1}{3}}}

Solution steps

\frac{\partial}{\partial x} ((x - 1)^{\frac{2}{3}} (y^{2} - 4))

Treat

y

as a constant

Take the constant out:

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

= (y^{2} - 4) \frac{\partial}{\partial x} ((x - 1)^{\frac{2}{3}})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x - 1) = 1

= (y^{2} - 4) \frac{2}{3 ( x - 1 ) ^{\frac{1}{3}}} \cdot 1

Simplify

(y^{2} - 4) \frac{2}{3 ( x - 1 ) ^{\frac{1}{3}}} \cdot 1 : \frac{2 ( y ^{2} - 4 )}{3 ( x - 1 ) ^{\frac{1}{3}}}

= \frac{2 ( y ^{2} - 4 )}{3 ( x - 1 ) ^{\frac{1}{3}}}

\frac{\partial}{\partial y} (y (x + y + 1))

\frac{d}{d x} ((x - 5)^{3})

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

\int \frac{4}{1 - x ^{2}} d x

\frac{d}{d x} (\frac{4 x ^{3} - 2 x + 1}{x ^{2}})

What is (\partial)/(\partial x)((x-1)^{2/3}(y^2-4)) ?
The answer to (\partial)/(\partial x)((x-1)^{2/3}(y^2-4)) is (2(y^2-4))/(3(x-1)^{1/3)}