Solve dn^2/(a_1^2-frac{d{2})}

$$\frac { d n ^ { 2 } } { ( a _ { 1 } ^ { 2 } - \frac { d } { 2 } ) }$$

Evaluate

$$\frac{2dn^{2}}{2a_{1}^{2}-d}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a_{1}^{2} times \frac{2}{2}.

$$\frac{dn^{2}}{\frac{2a_{1}^{2}}{2}-\frac{d}{2}}$$

Since \frac{2a_{1}^{2}}{2} and \frac{d}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{dn^{2}}{\frac{2a_{1}^{2}-d}{2}}$$

Divide dn^{2} by \frac{2a_{1}^{2}-d}{2} by multiplying dn^{2} by the reciprocal of \frac{2a_{1}^{2}-d}{2}.

$$\frac{dn^{2}\times 2}{2a_{1}^{2}-d}$$

Differentiate w.r.t. d

$$4\times \left(\frac{a_{1}n}{d-2a_{1}^{2}}\right)^{2}$$