Problem 897

Find the derivative of the function s = $\frac{1}{3\pi }$ sin(3t)- $\frac{1}{7\pi }$ cos(7t).

Solution:-

Use the rules of differentiation to find $\frac{ds}{dt}$ .

s = $\frac{1}{3\pi }$ sin(3t)- $\frac{1}{7\pi }$ cos(7t).

$\frac{ds}{dt}$ = $\frac{1}{3\pi }*\frac{d}{dt}(sin(3t))-\frac{1}{7\pi }*\frac{d}{dt}(cos(7t))$

To find $\frac{d}{dt}$ sin(3t) and $\frac{d}{dt}$ cos(7t), use the Chain Rule.

$\frac{d}{dt}$ (sin(3t)) = 3 cos(3t)

To find $\frac{d}{dt}$ (cos(7t)), use the Chain Rule.

$\frac{d}{dt}$ (cos(7t)) = -7sin(7t)

Substitute the expressions for $\frac{d}{dt}$ (sin(3t)) and and $\frac{d}{dt}(cos(7t))$ .

$\frac{ds}{dt}=\frac{1}{3\pi }*\frac{d}{dt}(sin(3t))-\frac{1}{7\pi }*\frac{d}{dt}(cos(7t))$

= $\frac{1}{3\pi }* (3cos(3t))-\frac{1}{7\pi }* (-7sin(7t))$

= $\frac{1}{\pi }(cos(3t))+sin(7t)$

Thus, $\frac{ds}{dt}=\frac{1}{\pi }(cos(3t)+sin(7t))$