Solve 5/4y6/4

$$\frac { 5 } { 4 } y \frac { 6 } { 4 }$$

Evaluate

$$\frac{15y}{8}$$

Solution Steps

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{4}y\times \frac{3}{2}$$

Multiply \frac{5}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{4\times 2}y$$

Do the multiplications in the fraction \frac{5\times 3}{4\times 2}.

$$\frac{15}{8}y$$

Differentiate w.r.t. y

$$\frac{15}{8} = 1\frac{7}{8} = 1.875$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5}{4}y\times \frac{3}{2})$$

Multiply \frac{5}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5\times 3}{4\times 2}y)$$

Do the multiplications in the fraction \frac{5\times 3}{4\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{15}{8}y)$$

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

$$\frac{15}{8}y^{1-1}$$

Subtract 1 from 1.

$$\frac{15}{8}y^{0}$$

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

$$\frac{15}{8}\times 1$$

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

$$\frac{15}{8}$$