Chapter 14 Multiple choice questions

* not completed

. Differentiate the following equation:
$y={\text{e}}^{8x}$.

\frac{\text{d}y}{\text{d}x}=8{\text{e}}^{7x} correct incorrect

\frac{\text{d}y}{\text{d}x}=8x\times {\text{e}}^{7x} correct incorrect

\frac{\text{d}y}{\text{d}x}=8{\text{e}}^{8x-1} correct incorrect

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

* not completed

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

\frac{\text{d}y}{\text{d}x}=\frac{1}{8}{\text{e}}^{\frac{x}{6}} correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{1}{8}{\text{e}}^{\frac{-5x}{6}} correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{x}{8}{\text{e}}^{\frac{x}{6}} correct incorrect

\frac{\text{d}y}{\text{d}x}=\frac{3}{4}{\text{e}}^{\frac{x}{6}} correct incorrect

* not completed

. Differentiate the following equation:$y=5\ln 4x$.

$\frac{\text{d}y}{\text{d}x}=\frac{20}{x}$ correct incorrect

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

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

$\frac{\text{d}y}{\text{d}x}=\frac{5}{4x}$ correct incorrect

* not completed

. Differentiate the following equation: $y=c\ln 8x+d{\text{e}}^{3x}$ ,
where c and d are constants.

$\frac{\text{d}y}{\text{d}x}=\frac{c}{8x}+3d{\text{e}}^{3x}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{8c}{x}+3dx{\text{e}}^{3x}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=8c+3d{\text{e}}^{3x}$ correct incorrect

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

* not completed

. Differentiate the following equation: y = 5 ln(8.2x) - 3 ln(2.1x ).

$\frac{\text{d}y}{\text{d}x}=\frac{5}{8.2x}-\frac{3}{2.1x}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{41}{x}-\frac{6.3}{x}$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=\frac{2}{6.1x}$ correct incorrect

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

* not completed

. Differentiate the following equation: y = sin 6x

$\frac{\text{d}y}{\text{d}x}=-6\cos 6x$ correct incorrect

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

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

$\frac{\text{d}y}{\text{d}x}=-\cos 6x$ correct incorrect

* not completed

. Differentiate the following equation: y = -4sin 2x.

$\frac{\text{d}y}{\text{d}x}=-8\cos x$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=8\cos 2x$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-8\cos 2x$ correct incorrect

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

* not completed

. Differentiate the following equation: y = cos (4.5x).

$\frac{\text{d}y}{\text{d}x}=-4.5\sin \left(4.5x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=4.5\sin \left(4.5x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-4.5\sin \left(x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=4.5\sin \left(x\right)$ correct incorrect

* not completed

. Differentiate the following equation: y = -5 cos (10x).

$\frac{\text{d}y}{\text{d}x}=-50\sin \left(x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=50\sin \left(x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=-50\sin \left(10x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=50\sin \left(10x\right)$ correct incorrect

* not completed

. Differentiate the following equation:
$y=\frac{\sin 9x}{3}-\frac{\cos 2x}{4}$.

$\frac{\text{d}y}{\text{d}x}=3\cos \left(3x\right)+\frac{1}{2}\sin \left(\frac{x}{2}\right)$ correct incorrect

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

$\frac{\text{d}y}{\text{d}x}=3\cos \left(9x\right)+\frac{1}{2}\sin \left(2x\right)$ correct incorrect

$\frac{\text{d}y}{\text{d}x}=3\cos \left(x\right)+\frac{1}{2}\sin \left(x\right)$ correct incorrect