Given that \(y=\dfrac{x^4}{\sqrt{1+2x}}\), find \(\dfrac{\mathrm dy}{\mathrm dx}\) in the form \(\dfrac{x^3(a+bx)}{(1+2x)^{3/2}}\), where \(a\) and \(b\) are integers.[4]
Given that \(y=x^2(x-1)^5\), find
\(\dfrac{\mathrm dy}{\mathrm dx}\),[3]
the range of values of \(x\) for which \(y\) is decreasing.[2]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.
Answer:(a) \(\dfrac{x^3(4+7x)}{(1+2x)^{3/2}}\). (b)(i) \(x(x-1)^4(7x-2)\). (ii) \(0<x<\dfrac27\).