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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Simplify

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

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

\frac{d}{d y} (y ln (y))

f (x) = 6 e^{x} cos (x), (0, 6)

\frac{d ^{2}}{d x ^{2}} (3 csc (x))

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

x \to 5 + lim (\frac{x ^{2} + 2}{5 - x})

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