Solve 5ab/2b*12b/10a

$$\frac { 5 a b } { 2 b } \cdot \frac { 12 b } { 10 a }$$

Evaluate

$$3b$$

Solution Steps

Cancel out b in both numerator and denominator.

$$\frac{5a}{2}\times \frac{12b}{10a}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5a}{2}\times \frac{6b}{5a}$$

Multiply \frac{5a}{2} times \frac{6b}{5a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5a\times 6b}{2\times 5a}$$

Cancel out 2\times 5a in both numerator and denominator.

$$3b$$

Differentiate w.r.t. b

$$3$$

Steps Using Definition of a Derivative

Cancel out b in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{5a}{2}\times \frac{12b}{10a})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{5a}{2}\times \frac{6b}{5a})$$

Multiply \frac{5a}{2} times \frac{6b}{5a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{5a\times 6b}{2\times 5a})$$

Cancel out 2\times 5a in both numerator and denominator.

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

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

$$3b^{1-1}$$

Subtract 1 from 1.

$$3b^{0}$$

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

$$3\times 1$$

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

$$3$$