Solve 4ab/3bdiv2a/6b

$$\frac { 4 a b } { 3 b } \div \frac { 2 a } { 6 b }$$

Evaluate

$$4b$$

Solution Steps

Divide \frac{4ab}{3b} by \frac{2a}{6b} by multiplying \frac{4ab}{3b} by the reciprocal of \frac{2a}{6b}.

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

Cancel out 2\times 3ab in both numerator and denominator.

$$2\times 2b$$

Multiply 2 and 2 to get 4.

$$4b$$

Differentiate w.r.t. b

$$4$$

Steps Using Definition of a Derivative

Divide \frac{4ab}{3b} by \frac{2a}{6b} by multiplying \frac{4ab}{3b} by the reciprocal of \frac{2a}{6b}.

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

Cancel out 2\times 3ab in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2\times 2b)$$

Multiply 2 and 2 to get 4.

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

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

$$4b^{1-1}$$

Subtract 1 from 1.

$$4b^{0}$$

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

$$4\times 1$$

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

$$4$$