Page:Calculus Made Easy.pdf/92

 Let $$u=(a^2-x^2)^{-\frac{1}{6}}$$ and $$v= (a^2-x^2)$$.

Let $$w=(a^2-x^2)^{\frac{1}{6}}$$ and $$z= (a^2+x^2)$$.

Hence

(9) Differentiate $$y^n$$ with respect to $$y^5$$.

(10) Find the first and second differential coefficients of $$y=\dfrac{x}{b}\sqrt{(a-x)x}$$.

Let $$\bigl[(a-x)x\bigr]^{\frac{1}{2}}=u$$ and let $$(a-x)x=w$$; then $$u=w^{\frac{1}{2}}$$.