Solve 66ab/8cdiv2a/12c

$$6 \frac { 6 a b } { 8 c } \div \frac { 2 a } { 12 c }$$

Evaluate

$$27b$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{6\times \frac{3ab}{4c}}{\frac{2a}{12c}}$$

Express 6\times \frac{3ab}{4c} as a single fraction.

$$\frac{\frac{6\times 3ab}{4c}}{\frac{2a}{12c}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{3\times 3ab}{2c}}{\frac{2a}{12c}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{3\times 3ab}{2c}}{\frac{a}{6c}}$$

Divide \frac{3\times 3ab}{2c} by \frac{a}{6c} by multiplying \frac{3\times 3ab}{2c} by the reciprocal of \frac{a}{6c}.

$$\frac{3\times 3ab\times 6c}{2ca}$$

Cancel out 2ac in both numerator and denominator.

$$3\times 3\times 3b$$

Multiply 3 and 3 to get 9.

$$9\times 3b$$

Multiply 9 and 3 to get 27.

$$27b$$

Differentiate w.r.t. b

$$27$$

Steps Using Definition of a Derivative

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{6\times \frac{3ab}{4c}}{\frac{2a}{12c}})$$

Express 6\times \frac{3ab}{4c} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{6\times 3ab}{4c}}{\frac{2a}{12c}})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{3\times 3ab}{2c}}{\frac{2a}{12c}})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{3\times 3ab}{2c}}{\frac{a}{6c}})$$

Divide \frac{3\times 3ab}{2c} by \frac{a}{6c} by multiplying \frac{3\times 3ab}{2c} by the reciprocal of \frac{a}{6c}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{3\times 3ab\times 6c}{2ca})$$

Cancel out 2ac in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3\times 3\times 3b)$$

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}b}(9\times 3b)$$

Multiply 9 and 3 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}b}(27b)$$

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

$$27b^{1-1}$$

Subtract 1 from 1.

$$27b^{0}$$

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

$$27\times 1$$

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

$$27$$