Given that the equations of two curves are $y = \frac{2}{5} x^{3} + 4x + 5$ and \(z = \frac{1}{2}

Question

Given that the equations of two curves are $y = \frac{2}{5} x^{3} + 4x + 5$ and $z = \frac{1}{2} x^{4} - 3x^{2} + 4x$, respectively, find the rates of change of $y$ and $z$ with respect to $x$ when $x = 2$.

Accepted Answer

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{44}{5},\ \dfrac{\mathrm{d}z}{\mathrm{d}x}=8$

Differentiation - Derivative as an Instantaneous Rate of Change

Differentiation - Derivative as an Instantaneous Rate of Change

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