<p>Given that $y={{x}^{4}}-4x$</p>
<ol class="i-list"><li><div class="list-item-paragraph">Show that $y$ is decreasing for $x&lt;1$.</div></li><li><div class="list-item-paragraph">Find $\frac{\mathrm{d}y}{\mathrm{d}x}$, $\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}$ and ${{\left( \frac{\mathrm{d}y}{\mathrm{d}x} \right)}^{2}}$, respectively.</div></li></ol>

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$, $\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}$ and ${{\left( \frac{\mathrm{d}y}{\mathrm{d}x} \right)}^{2}}$, respectively.

Applications of Differentiation

Question fad8d496