Solve ab/10*5/a=

$$\frac { a b } { 10 } \times \frac { 5 } { a } =$$

Evaluate

$$\frac{b}{2}$$

Solution Steps

Multiply \frac{ab}{10} times \frac{5}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{ab\times 5}{10a}$$

Cancel out 5a in both numerator and denominator.

$$\frac{b}{2}$$

Differentiate w.r.t. b

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Multiply \frac{ab}{10} times \frac{5}{a} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5a in both numerator and denominator.

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

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

$$\frac{1}{2}b^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}b^{0}$$

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

$$\frac{1}{2}\times 1$$

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

$$\frac{1}{2}$$