Solve (t+x/v)]quadtext{and}quadthereforey=asin[2pi/lambda(vt+x)]

$$( t + \frac { x } { v } ) ] \quad \text { and } \quad \therefore y = a \sin [ \frac { 2 \pi } { \lambda } ( v t + x ) ]$$

Evaluate

$$t+\frac{x}{v}$$

Solution Steps

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

$$\frac{tv}{v}+\frac{x}{v}$$

Since \frac{tv}{v} and \frac{x}{v} have the same denominator, add them by adding their numerators.

$$\frac{tv+x}{v}$$

Differentiate w.r.t. x

$$\frac{1}{v}$$