Differentiate (a cos 3 t) w.r.t. to (a sin 3 t)
| Differentiate (a cos3t) w.r.t. to (a sin3 t)
A. cot t
B. –cot t
C. tan t
D. –tan t
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
For two functions defined as a function of time (t) as shown:
u = f(t) and v = g(t)
The differentiation of u with respect to v is given by:
\(\frac{du}{dv}=\frac{du/dt}{dv/dt}\)
Calculation:
Given u = a cos3t and v = a sin3t
\(\frac{du}{dt}=-3a(cos^2t)(sint)\)
\(\frac{dv}{dt}=3a(sin^2t)(cost)\)
\(\frac{du}{dv}=\frac{-3a(cos^2t)(sint)}{3a(sin^2t)(cost)}\)
\(\frac{du}{dv}=-cot~t\)