√(48.x⁵) = √[(8)(6)(x⁴)(x¹)] =√[(2².2)(6)(x⁴)(x)] =2x²√(2)(6)(x)
=2x²√12x
If
then by the product rule,
and by the chain rule,
which leaves us with
Alternatively, if you exclusively want to use the chain rule, you can carry out logarithmic differentiation:
By the chain rule, differentiating both sides with respect to <em>x</em> gives
Solve for <em>f'(x)</em> yields
just as before.