What is the derivative of 1/3 sqrt(y)(y-3) ?

The derivative of 1/3 sqrt(y)(y-3) is (y-1)/(2sqrt(y))

What is the first derivative of 1/3 sqrt(y)(y-3) ?

The first derivative of 1/3 sqrt(y)(y-3) is (y-1)/(2sqrt(y))

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derivative of

\frac{1}{3} y (y - 3)

\frac{y - 1}{2 y}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = y - 3

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

\frac{d}{d y} (y) = \frac{1}{2 y}

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

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

Simplify

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

= \frac{y - 1}{2 y}

x \to 1 lim (x^{2} - 2 x + 2)

\int (cos (t) sin (t)) d t

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

\int_{1}^{8} x^{\frac{- 2}{3}} d x

e^{- x} sin (x)

What is the derivative of 1/3 sqrt(y)(y-3) ?
The derivative of 1/3 sqrt(y)(y-3) is (y-1)/(2sqrt(y))
What is the first derivative of 1/3 sqrt(y)(y-3) ?
The first derivative of 1/3 sqrt(y)(y-3) is (y-1)/(2sqrt(y))