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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d y} (y^{2} + 2) = 2 y

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

Simplify

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

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

\int cos (2) d x

\int cos^{4} (x) sin^{2} (x) d x

\int_{0}^{3} sin (x^{2}) d x

\frac{d y}{d x} = y^{2} + y

y = arccos (x)

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