Show that the derivative of $x(x-3)^4$ with respect to $x$ is $(5x-3)(x-3)^3$.[2] Hence, given

Question

Show that the derivative of $x(x-3)^4$ with respect to $x$ is $(5x-3)(x-3)^3$.[2] 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 $x=1$. [4]

Accepted Answer

(a) $\frac{d}{dx}[x(x-3)^4]=(5x-3)(x-3)^3$ (b) $\frac{dx}{dt}=2.50\text{ units/s}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

Solution:

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