Page:Calculus Made Easy.pdf/173

 (10) $$y=\dfrac{1}{\log_\epsilon x}$$.

(11) $$y=\sqrt[3]{\log_\epsilon x} = (\log_\epsilon x)^{\frac{1}{3}}$$. Let $$y=z^{\frac{1}{3}}$$.

(12) $$y=\left(\dfrac{1}{a^x}\right)^{ax}$$.

Try now the following exercises.

Exercises XII. (See page 260 for Answers.)

(1) Differentiate $$y=b(\epsilon^{ax} -\epsilon^{-ax})$$.

(2) Find the differential coefficient with respect to $$t$$ of the expression $$u=at^2+2\log_\epsilon t$$.

(3) if $$y=n^t$$, find $$\dfrac{d(\log_\epsilon y)}{dt}$$.

(4) Show that if $$y=\dfrac{1}{b}\cdot \dfrac{a^{bx}}{\log_\epsilon a}$$ ; $$\dfrac{dy}{dx}=a^{bx}$$.

(5) If $$w=pv^n$$, find $$\dfrac{dw}{dv}$$.