Page:Calculus Made Easy.pdf/91

 (7) Differentiate $$y=(x+\sqrt{x^2+x+a})^3$$.

Let $$x+\sqrt{x^2+x+a}=u$$.

Now let $$(x^2+x+a)^{\tfrac{1}{2}}=v$$ and $$ (x^2+x+a)=w$$.

(8) Differentiate $$y=\sqrt{\dfrac{a^2+x^2}{a^2-x^2}} \sqrt[3]{\dfrac{a^2-x^2}{a^2+x^2}}$$.

We get