Page:Calculus Made Easy.pdf/63

 (6) Differentiate $$y=0.5x^3(x-3)$$

Same remarks as for preceding example.

(7) Differentiate $$w=\left(\theta+\dfrac{1}{\theta}\right)\left(\sqrt{\theta}+\dfrac{1}{\sqrt{\theta}}\right)$$

This may be written $w=(\theta+\theta^{-1})(\theta^{\frac{1}{2}} + \theta^{-\frac{1}{2}})$.|undefined

This, again, could be obtained more simply by multiplying the two factors first, and differentiating afterwards. This is not, however, always possible; see, for instance, p. 173, example 8, in which the rule for differentiating a product must be used.

(8) Differentiate $$y=\frac{a}{1+a\sqrt{x}+a^2x}$$.