Chapter 13 Multiple choice questions

* not completed

. Given that y=axⁿ. Select the correct form for the differential \frac{\text{d}y}{\text{d}x}
from the list below:

\frac{\text{d}y}{\text{d}x}=n\times x^{n-1} correct incorrect

\frac{\text{d}y}{\text{d}x}=a\times x^{n-1} correct incorrect

\frac{\text{d}y}{\text{d}x}=a\times n\times x^{n-1} correct incorrect

\frac{\text{d}y}{\text{d}x}=a\times n\times x^{n+1} correct incorrect

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. Differentiate the following equation using the standard rules: y=x⁹.

\frac{\text{d}y}{\text{d}x}=x^8 correct incorrect

\frac{\text{d}y}{\text{d}x}=9x^8 correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{x^{10}}{10} correct incorrect

\frac{\text{d}y}{\text{d}x}=8x^9 correct incorrect

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. Differentiate the following equation: y = 6x^-3.

\frac{\text{d}y}{\text{d}x}=-18x^{-4} correct incorrect

\frac{\text{d}y}{\text{d}x}=-18x^{-2} correct incorrect

\frac{\text{d}y}{\text{d}x}=-12x^{-3} correct incorrect

\frac{\text{d}y}{\text{d}x}=-3x^{-2} correct incorrect

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. Differentiate the following equation: p = 4q^4.2

\frac{\text{d}p}{\text{d}q}=12.8x^{4.2} correct incorrect

\frac{\text{d}p}{\text{d}q}=3x^{3.2} correct incorrect

\frac{\text{d}p}{\text{d}q}=4x^{2.2} correct incorrect

\frac{\text{d}p}{\text{d}q}=12.8x^{2.2} correct incorrect

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. Differentiate the following equation: $y=4\sqrt{x}$.

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

\frac{\text{d}y}{\text{d}x}=\frac{2}{x^{\frac{-1}{2}}} correct incorrect

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

\frac{\text{d}y}{\text{d}x}=\frac{8}{3}{x}^{\frac{3}{2}} correct incorrect

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

\frac{\text{d}y}{\text{d}x}=\frac{-12}{\sqrt{x^5}} correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{-24}{x^{\frac{5}{2}}} correct incorrect

\frac{\text{d}y}{\text{d}x}=12x^{\frac{1}{2}} correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{-12}{x^{\frac{1}{2}}} correct incorrect

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. Differentiate the following equation: $y=5-\frac{9}{x^7}$.

\frac{\text{d}y}{\text{d}x}=5-\frac{63}{x^8} correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{63}{x^6} correct incorrect

\frac{\text{d}y}{\text{d}x}=5x+\frac{63}{x^6} correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{63}{x^8} correct incorrect

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. Differentiate the following equation: $y=12\sqrt{x^3}+8$.

\frac{\text{d}y}{\text{d}x}=18x correct incorrect

\frac{\text{d}y}{\text{d}x}=18\sqrt{x^5}+8x correct incorrect

\frac{\text{d}y}{\text{d}x}=8x+12\sqrt{x} correct incorrect

\frac{\text{d}y}{\text{d}x}=18\sqrt{x} correct incorrect

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. Differentiate the following equation: $s=14t^3-\frac{t^2}{6}+5t-3$.

\frac{\text{d}s}{\text{d}t}=42t^4-\frac{t^3}{3}+5t^2-3t correct incorrect

\frac{\text{d}s}{\text{d}t}=42t^2-\frac{t}{3}+5 correct incorrect

\frac{\text{d}s}{\text{d}t}=42t^2-\frac{t}{6} correct incorrect

\frac{\text{d}s}{\text{d}t}=14t^2-\frac{t}{3}+2 correct incorrect

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. Differentiate the following equation: $m=\frac{-8}{v^6}+\frac{v^4}{5}+\frac{1}{7}$.

$\frac{\text{d}m}{\text{d}v}=\frac{48}{v^5}+\frac{4v^3}{5}$ correct incorrect

$\frac{\text{d}m}{\text{d}v}=\frac{48}{v^7}+\frac{v^3}{20}$ correct incorrect

$\frac{\text{d}m}{\text{d}v}=\frac{48}{v^7}+\frac{4v^3}{5}$ correct incorrect

$\frac{\text{d}m}{\text{d}v}=\frac{48}{v^7}+\frac{4v^3}{5}+\frac{v}{7}$ correct incorrect