Chapter 16 Multiple choice questions

* not completed

. Differentiate the following equation: y = 5x³ ln 2x.

$\frac{\mathrm{d}y}{\mathrm{d}x}=15x^2\ln 2x$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=15x$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=15x^3+15x^2\ln 2x$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=5x^2\left(1+31\mathrm{n}2x\right)$ correct incorrect

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. Differentiate the following equation: y = x⁴e^7x.

$\frac{\mathrm{d}y}{\mathrm{d}x}=21x^3{\mathrm{e}}^{7x}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=x^3{\mathrm{e}}^{7x}\left(7x+4\right)$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=x^3\left(7x{\mathrm{e}}^{7x}+4{\mathrm{e}}^{6x}\right)$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=28x^5{\mathrm{e}}^{7x}$ correct incorrect

* not completed

. Differentiate the following equation: y = e^5x sin (9x).

$\frac{\mathrm{d}y}{\mathrm{d}x}={\mathrm{e}}^{5x}\left(5\sin 9x+9\cos 9x\right)$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=5{\mathrm{e}}^{5x}\sin 9\mathrm{x}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=45{\mathrm{e}}^{5x}\cos 9x+{\mathrm{e}}^{5x}\sin 9x$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}={\mathrm{e}}^{5x}\left(\sin 9x\mathit{ }\mathit{-}\mathit{ }9\mathit{ }\cos \mathit{ }9x\right)$ correct incorrect

* not completed

. Differentiate the following equation: $y=\ln \left(4x\right)\cos \left(\sqrt{x}\right)$.

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{2x}\left(2\cos \left(\sqrt{x}\right)+\sqrt{x}\ln \left(4x\right)\sin \left(\sqrt{x}\right)\right)$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{2x}\left(2\cos \left(\sqrt{x}\right)-\sqrt{x}\ln \left(4x\right)\sin \left(\sqrt{x}\right)\right)$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{2}\left(2\cos \left(\sqrt{x}\right)-\sqrt{x}\ln \left(4x\right)\sin \left(\sqrt{x}\right)\right)$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{2x}\left(2\cos \left(\sqrt{x}\right)-\sqrt{x}\ln \left(4x\right)\sin \left(\sqrt{x}\right)\right)$ correct incorrect

* not completed

. Differentiate the following equation: y = sin³ (4x) cos⁵ (3x).

$\frac{\mathrm{d}y}{\mathrm{d}x}=3{\cos }^4\left(3x\right){\sin }^2\left(4x\right)\left(5\sin \left(3x\right)\sin \left(4x\right)-4\cos \left(3x\right)\cos \left(4x\right)\right)$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=3{\cos }^5\left(3x\right){\sin }^3\left(4x\right)\left(-5\sin \left(3x\right)\sin \left(4x\right)+4\cos \left(3x\right)\cos \left(4x\right)\right)$ correct incorrect

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

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

* not completed

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

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{x^4(5\ln 7x-1)}{\left(\ln 7x\right)}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{x^4(5\ln 7x-1)}{(\ln 7x{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{(5x^4\ln 7x-x^5)}{(\ln 7x{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{x^4(5\ln 7x+1)}{(\ln 7x{)}^2}$ correct incorrect

* not completed

. Differentiate the following equation: $y=\frac{\ln 5x}{\sin 4x}$.

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\sin {\displaystyle }{\displaystyle 4}{\displaystyle x}{\displaystyle }{\displaystyle -}{\displaystyle }{\displaystyle 4}{\displaystyle }{\displaystyle 1}{\displaystyle \mathrm{n}}{\displaystyle }{\displaystyle 5}{\displaystyle x}{\displaystyle }{\displaystyle \cos }{\displaystyle }{\displaystyle 4}{\displaystyle x}}{x(\sin 4x{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\sin {\displaystyle 4}x{\displaystyle -}{\displaystyle 4}x{\displaystyle 1}{\displaystyle \mathrm{n}}{\displaystyle 5}{\displaystyle x}{\displaystyle \cos }{\displaystyle 4}{\displaystyle x}}{(\sin 4x{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{x\left(\sin 4x\right)}-\frac{4\ln 5x\cos 4x}{{\displaystyle (\sin {\displaystyle }{\displaystyle 4}{\displaystyle x}{)}^2}}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\sin {\displaystyle }{\displaystyle 4}{\displaystyle x}{\displaystyle }{\displaystyle +}{\displaystyle }{\displaystyle 4}{\displaystyle x}{\displaystyle }{\displaystyle 1}{\displaystyle \mathrm{n}}{\displaystyle }{\displaystyle 5}{\displaystyle x}{\displaystyle }{\displaystyle \cos }{\displaystyle }{\displaystyle 4}{\displaystyle x}}{x(\sin 4x{)}^2}$ correct incorrect

* not completed

. Differentiate the following equation: $y=\frac{{\mathrm{e}}^{6x}}{\cos x^2}$.

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{6{\mathrm{e}}^{6x}}{{\displaystyle (\cos {\displaystyle }{\displaystyle {{\displaystyle x}}^2}{)}^2}}+\frac{2x{\mathrm{e}}^{6x}\sin x^2}{{\displaystyle (\cos {\displaystyle }{\displaystyle {{\displaystyle x}}^2}{)}^2}}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{6{\mathrm{e}}^{6x}}{{\displaystyle \left(\cos x^2\right)}}+\frac{2x{\mathrm{e}}^{6x}\sin x^2}{{\displaystyle (\cos x^2{)}^2}}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{6{\mathrm{e}}^{6x}}{{\displaystyle (\cos {\displaystyle }{\displaystyle {{\displaystyle x}}^2}{)}^2}}-\frac{2x{\mathrm{e}}^{6x}\sin x^2}{{\displaystyle (\cos {\displaystyle }{\displaystyle {{\displaystyle x}}^2}{)}^2}}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{6{\mathrm{e}}^{6x}}{{\displaystyle \left(\cos x^2\right)}}-\frac{2x{\mathrm{e}}^{6x}\sin x^2}{{\displaystyle (\cos x^2{)}^2}}$ correct incorrect

* not completed

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

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{-4\sin 4x}{{\displaystyle \left(\sin 2x\right)}}-\frac{2\cos 2x\cos 4x}{{\displaystyle (\sin 2x{)}^2}}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{-2(2\sin 2x\sin 4x-\cos 2x\cos 4x)}{(\sin 2x{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{-4\sin 4x}{{\displaystyle \left(\sin 2x\right)}}+\frac{2\cos 2x\cos 4x}{{\displaystyle (\sin 2x{)}^2}}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{(-4\sin 2x\sin 4x-\cos 2x\cos 4x)}{(\sin 2x{)}^2}$ correct incorrect

* not completed

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

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\left(6x^4\ln \right(5x^2)-1)\exp \left(3x^4\right)}{x(\ln 5x^2{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{12x^3\exp \left(3x^{\mathit{4}}\right)}{\left(\ln 5x^2\right)}+\frac{2\exp \left(3x^4\right)}{x(\ln 5x^2{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{2\left(6x^4\ln \right(5x^2)+1)\exp \left(3x^4\right)}{x(\ln 5x^2{)}^2}$ correct incorrect

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{12x^3\exp \left(3x^{\mathit{4}}\right)}{\left(\ln 5x^2\right)}-\frac{2\exp \left(3x^4\right)}{x(\ln 5x^2{)}^2}$ correct incorrect