What is the d/(dy)((4-y)^{1/3}) ?

The d/(dy)((4-y)^{1/3}) is -1/(3(4-y)^{2/3)}

What is the first d/(dy)((4-y)^{1/3}) ?

The first d/(dy)((4-y)^{1/3}) is -1/(3(4-y)^{2/3)}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d y} (4 - y) = - 1

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

Simplify

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

What is the d/(dy)((4-y)^{1/3}) ?
The d/(dy)((4-y)^{1/3}) is -1/(3(4-y)^{2/3)}
What is the first d/(dy)((4-y)^{1/3}) ?
The first d/(dy)((4-y)^{1/3}) is -1/(3(4-y)^{2/3)}