Solve b^2/4a/(-frac{b{2a}+b/a)}

$$\frac { \frac { b ^ { 2 } } { 4 a } } { ( - \frac { b } { 2 a } + \frac { b } { a } ) }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and a is 2a. Multiply \frac{b}{a} times \frac{2}{2}.

$$\frac{\frac{b^{2}}{4a}}{-\frac{b}{2a}+\frac{2b}{2a}}$$

Since -\frac{b}{2a} and \frac{2b}{2a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{b^{2}}{4a}}{\frac{-b+2b}{2a}}$$

Combine like terms in -b+2b.

$$\frac{\frac{b^{2}}{4a}}{\frac{b}{2a}}$$

Divide \frac{b^{2}}{4a} by \frac{b}{2a} by multiplying \frac{b^{2}}{4a} by the reciprocal of \frac{b}{2a}.

$$\frac{b^{2}\times 2a}{4ab}$$

Cancel out 2ab in both numerator and denominator.

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

Differentiate w.r.t. b

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

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and a is 2a. Multiply \frac{b}{a} times \frac{2}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{b^{2}}{4a}}{-\frac{b}{2a}+\frac{2b}{2a}})$$

Since -\frac{b}{2a} and \frac{2b}{2a} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{b^{2}}{4a}}{\frac{-b+2b}{2a}})$$

Combine like terms in -b+2b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{b^{2}}{4a}}{\frac{b}{2a}})$$

Divide \frac{b^{2}}{4a} by \frac{b}{2a} by multiplying \frac{b^{2}}{4a} by the reciprocal of \frac{b}{2a}.

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

Cancel out 2ab 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.

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