Page:Calculus Made Easy.pdf/87



one is stumped by finding that the expression to be differentiated is too complicated to tackle directly.

Thus, the equation $y=(x^2+a^2)^\tfrac {3}{2}$ is awkward to a beginner.

Now the dodge to turn the difficulty is this: Write some symbol, such as $$u$$, for the expression $$x^2+a^2$$; then the equation becomes $y=u^\tfrac {3}{2}$, which you can easily manage; for $\frac{dy}{du}=\frac {3}{2}u^{\tfrac {1}{2}}$.|undefined Then tackle the expression $u=x^2+a^2$, and differentiate it with respect to $$x$$, $\frac {du}{dx}=2x$.