Page:Calculus Made Easy.pdf/192

 (2) $$y=\cos^3 \theta$$.

This is the same thing as $$y=(\cos \theta)^3$$.

Let $$\cos\theta=v$$; then $$y=v^3$$; $$\dfrac{dy}{dv}=3v^2$$.

(3) $$y=\sin(x+a)$$.

Let $$x+a=v$$; then $$y=\sin v$$.

(4) $$y=\log_\epsilon \sin \theta$$.

Let $$\sin\theta=v$$; $$y=\log_\epsilon v$$.

(5) $$y=\cot\theta=\dfrac{\cos\theta}{\sin\theta}$$.

(6) $$y=\tan 3\theta$$.

Let $$3\theta=v$$; $$y=\tan v$$ ;$$\dfrac{dy}{dv}=\sec^2 v$$.