Chapter 15 Multiple choice questions

* not completed

. Differentiate the following equation:
$y={\left(2x^5+4x^3+\frac{x}{2}\right)}^4$.

$\frac{\text{d}y}{\text{d}x}=4\left(10x^4+12x^2+\frac{1}{2}\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=4\left(10x^4+12x^2+\frac{1}{2}\right){\left(2x^5+4x^3+\frac{x}{2}\right)}^3$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=4{\left(2x^5+4x^3+\frac{x}{2}\right)}^3$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=4\left(10x^6+12x^4+\frac{x^2}{2}\right){\left(2x^5+4x^3+\frac{x}{2}\right)}^3$ correct incorrect

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. Differentiate the following equation:
$y=3{\text{e}}^{4x^6}$.

$3{\text{e}}^{4x^6}$ correct incorrect

$72x^5{\text{e}}^{4x^6}$ correct incorrect

$24x^5{\text{e}}^{4x^6}$ correct incorrect

$12x^6{\text{e}}^{4x^6}$ correct incorrect

* not completed

. Differentiate the following equation:
$y=3\ln \left(4x^7\right)$.

$\frac{\text{d}y}{\text{d}x}=\frac{84}{x}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{84}{x^7}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{12}{x^6}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{21}{x}$ correct incorrect

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. Differentiate the following equation:
$y=9\ln \left(\sqrt{x^7}\right)$.

$\frac{\text{d}y}{\text{d}x}=\frac{9}{\sqrt{x^7}}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{9}{\sqrt{x^9}}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{63}{2x}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{63}{\sqrt{x^5}}$ correct incorrect

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. Differentiate the following equation:
$y=5\sin \left(4x^2+9x^3\right)$.

\frac{\text{d}y}{\text{d}x}=\left(40x+135x^2\right)\cos \left(4x^2+9x^3\right) correct incorrect

\frac{\text{d}y}{\text{d}x}=40x\cos \left(4x^2+9x^3\right) correct incorrect

\frac{\text{d}y}{\text{d}x}=-40x\cos \left(4x^2+9x^3\right) correct incorrect

\frac{\text{d}y}{\text{d}x}=-40x+135x^2\cos \left(4x^2+9x^3\right) correct incorrect

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. Differentiate the following equation:
$y=\cos \left(4{\text{e}}^{2x}\right)$.

$\frac{\text{d}y}{\text{d}x}=8{\text{e}}^{2x}\sin \left({\text{4e}}^x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=8{\text{e}}^{2x}\sin \left(4{\text{e}}^{2x}\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-8{\text{e}}^{2x}\sin \left({\text{4e}}^x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-8{\text{e}}^{2x}\sin \left(4{\text{e}}^{2x}\right)$ correct incorrect

* not completed

. Differentiate the following equation:
$y=-2\cos \left(\frac{3}{x}-\frac{4}{x^2}\right)$.

$\frac{\text{d}y}{\text{d}x}=\left(\frac{6}{x^2}-\frac{16}{x^3}\right)\sin \left(\frac{3}{x}-\frac{4}{x^2}\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\left(-\frac{6}{x}+\frac{16}{x^2}\right)\sin \left(\frac{3x-4}{x^2}\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\left(\frac{6}{x}-\frac{16}{x^2}\right)\sin \left(\frac{3}{x}-\frac{4}{x^2}\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\left(-\frac{6}{x^2}+\frac{16}{x^3}\right)\sin \left(\frac{3x-4}{x^2}\right)$ correct incorrect

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. Differentiate the following equation: $y=\exp \left(\sin 3x\right)$.

$\frac{\text{d}y}{\text{d}x}=3{\text{e}}^{\sin 3x}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=3{\text{e}}^{\sin 3x}\sin 3x$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=3{\text{e}}^{\sin 3x}\cos 3x$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-3{\text{e}}^{\sin 3x}\cos 3x$ correct incorrect

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. Differentiate the following equation:
$y=\exp \left({\cos }^{3}5x\right)$.

$\frac{\text{d}y}{\text{d}x}=-15\sin \left(5x\right)\exp \left({\cos }^3\left(5x\right)\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-15\sin \left(5x\right){\cos }^2\left(5x\right)\exp \left({\cos }^3\left(5x\right)\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-15\sin \left(5x\right)\cos \left(5x\right)\exp \left({\cos }^3\left(5x\right)\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-15{\cos }^2\left(5x\right)\exp \left({\cos }^3\left(5x\right)\right)$ correct incorrect

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. Differentiate the following equation:
$y=\sin \left(5\text{exp}\left(x^4\right)\right)$.

$\frac{\text{d}y}{\text{d}x}=5\exp \left(x^4\right)\times \cos \left(5\exp \left(x^4\right)\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=20x^3\times \exp \left(x^4\right)\times \cos \left(5\exp \left(x^4\right)\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=20x^3\times \exp \left(x^4\right)\times \sin \left(5\exp \left(x^4\right)\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=20x^3\times \exp \left(x^4\right)\times \cos \left(\exp \left(x^4\right)\right)$ correct incorrect