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Popular >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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