Solve d(1/t+frac{1{t}})

$$d ( \frac { 1 } { t + \frac { 1 } { t } } )$$

Evaluate

$$\frac{dt}{t^{2}+1}$$

Short Solution Steps

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

$$d\times \frac{1}{\frac{tt}{t}+\frac{1}{t}}$$

Since \frac{tt}{t} and \frac{1}{t} have the same denominator, add them by adding their numerators.

$$d\times \frac{1}{\frac{tt+1}{t}}$$

Do the multiplications in tt+1.

$$d\times \frac{1}{\frac{t^{2}+1}{t}}$$

Divide 1 by \frac{t^{2}+1}{t} by multiplying 1 by the reciprocal of \frac{t^{2}+1}{t}.

$$d\times \frac{t}{t^{2}+1}$$

Express d\times \frac{t}{t^{2}+1} as a single fraction.

$$\frac{dt}{t^{2}+1}$$

Differentiate w.r.t. d

$$\frac{t}{t^{2}+1}$$