Solve 4a/3*18b/2a

$$\frac { 4 a } { 3 } \times \frac { 18 b } { 2 a }$$

Evaluate

$$12b$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{4a}{3}\times \frac{9b}{a}$$

Multiply \frac{4a}{3} times \frac{9b}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4a\times 9b}{3a}$$

Cancel out 3a in both numerator and denominator.

$$3\times 4b$$

Multiply 3 and 4 to get 12.

$$12b$$

Differentiate w.r.t. b

$$12$$

Steps Using Definition of a Derivative

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{4a}{3}\times \frac{9b}{a})$$

Multiply \frac{4a}{3} times \frac{9b}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{4a\times 9b}{3a})$$

Cancel out 3a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3\times 4b)$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}b}(12b)$$

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

$$12b^{1-1}$$

Subtract 1 from 1.

$$12b^{0}$$

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

$$12\times 1$$

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

$$12$$