Solve 3/515y/6

$$\frac { 3 } { 5 } \frac { 15 y } { 6 }$$

Evaluate

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

Solution Steps

Divide 15y by 6 to get \frac{5}{2}y.

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

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

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

Cancel out 5 in both numerator and denominator.

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

Differentiate w.r.t. y

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using Definition of a Derivative

Divide 15y by 6 to get \frac{5}{2}y.

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

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

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

Cancel out 5 in both numerator and denominator.

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

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

$$\frac{3}{2}y^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{2}y^{0}$$

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

$$\frac{3}{2}\times 1$$

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

$$\frac{3}{2}$$