<ol class="abc-list"><li><div class="list-item-paragraph">Show that the derivative of $x(x-3)^4$ with respect to $x$ is $(5x-3)(x-3)^3$<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Hence, given that $y=\frac{x(x-3)^4}{5x-3}$ and $y$ is decreasing at a constant rate of $70$ units/s, calculate the rate of change of $x$ when $x=1$.<span class="inline-marks">[4]</span></div></li></ol>

Show that the derivative of $x(x-3)^4$ with respect to $x$ is $(5x-3)(x-3)^3$

Hence, given that $y=\frac{x(x-3)^4}{5x-3}$ and $y$ is decreasing at a constant rate of $70$ units/s, calculate the rate of change of $x$ when $x=1$.

Techniques of Differentiation

Techniques of Differentiation