Page:Calculus Made Easy.pdf/93

 ::$$\frac{dw}{dx}=a-2x$$.


 * $$\frac{du}{dw}\times{\frac{dw}{dx}}=\frac{du}{dx} =\frac{a-2x}{2\sqrt{(a-x)x}}$$.

Hence

Now

(We shall need these two last differential coefficients later on. See Ex. X. No. 11)

Exercises VI. (See page 257 for Answers.)

Differentiate the following:

(1) $$y=\sqrt{x^2+1}$$.

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

(3) $$y=\dfrac{1}{\sqrt{a+x}}$$.

(4) $$y=\dfrac{a}{\sqrt{a-x^2}}$$.

(5) $$y=\dfrac{\sqrt{x^2-a^2}}{x^2}$$.

(6) $$y=\dfrac{\sqrt[3]{x^4+a}}{\sqrt[2]{x^3+a}}$$.

(7) $$y=\dfrac{a^2+x^2}{(a+x)^2}$$.