Solve 4/7div6/7quady8/9div1/4

$$\frac { 4 } { 7 } \div \frac { 6 } { 7 } \quad y \frac { 8 } { 9 } \div \frac { 1 } { 4 }$$

Evaluate

$$\frac{64y}{27}$$

Solution Steps

Divide \frac{4}{7} by \frac{6}{7} by multiplying \frac{4}{7} by the reciprocal of \frac{6}{7}.

$$\frac{\frac{4}{7}\times \frac{7}{6}y\times \frac{8}{9}}{\frac{1}{4}}$$

Multiply \frac{4}{7} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 7}{7\times 6}y\times \frac{8}{9}}{\frac{1}{4}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{\frac{4}{6}y\times \frac{8}{9}}{\frac{1}{4}}$$

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

$$\frac{\frac{2}{3}y\times \frac{8}{9}}{\frac{1}{4}}$$

Multiply \frac{2}{3} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\times 8}{3\times 9}y}{\frac{1}{4}}$$

Do the multiplications in the fraction \frac{2\times 8}{3\times 9}.

$$\frac{\frac{16}{27}y}{\frac{1}{4}}$$

Divide \frac{16}{27}y by \frac{1}{4} by multiplying \frac{16}{27}y by the reciprocal of \frac{1}{4}.

$$\frac{16}{27}y\times 4$$

Express \frac{16}{27}\times 4 as a single fraction.

$$\frac{16\times 4}{27}y$$

Multiply 16 and 4 to get 64.

$$\frac{64}{27}y$$

Differentiate w.r.t. y

$$\frac{64}{27} = 2\frac{10}{27} = 2.3703703703703702$$

Steps Using Definition of a Derivative

Divide \frac{4}{7} by \frac{6}{7} by multiplying \frac{4}{7} by the reciprocal of \frac{6}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{4}{7}\times \frac{7}{6}y\times \frac{8}{9}}{\frac{1}{4}})$$

Multiply \frac{4}{7} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{4\times 7}{7\times 6}y\times \frac{8}{9}}{\frac{1}{4}})$$

Cancel out 7 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{4}{6}y\times \frac{8}{9}}{\frac{1}{4}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{2}{3}y\times \frac{8}{9}}{\frac{1}{4}})$$

Multiply \frac{2}{3} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{2\times 8}{3\times 9}y}{\frac{1}{4}})$$

Do the multiplications in the fraction \frac{2\times 8}{3\times 9}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{16}{27}y}{\frac{1}{4}})$$

Divide \frac{16}{27}y by \frac{1}{4} by multiplying \frac{16}{27}y by the reciprocal of \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{16}{27}y\times 4)$$

Express \frac{16}{27}\times 4 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{16\times 4}{27}y)$$

Multiply 16 and 4 to get 64.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{64}{27}y)$$

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

$$\frac{64}{27}y^{1-1}$$

Subtract 1 from 1.

$$\frac{64}{27}y^{0}$$

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

$$\frac{64}{27}\times 1$$

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

$$\frac{64}{27}$$