Solve 3/5y2/3=

$$3 / 5 y 2 / 3 =$$

Evaluate

$$\frac{2y}{5}$$

Solution Steps

Multiply \frac{3}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{5\times 3}y$$

Cancel out 3 in both numerator and denominator.

$$\frac{2}{5}y$$

Differentiate w.r.t. y

$$\frac{2}{5} = 0.4$$

Steps Using Definition of a Derivative

Multiply \frac{3}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3\times 2}{5\times 3}y)$$

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{5}y)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{2}{5}y^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{5}y^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{2}{5}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{2}{5}$$