Differentiation — Quiz 2

Questions in this quiz (10)

1. Find $$\frac{d}{dx}\left(\sqrt[3]{x^4+2x-e^x}\right)$$.

   • $$\frac{4x^3+2-e^x}{3(x^4+2x-e^x)^{1/3}}$$
   • $$\frac{4x^3+2-e^x}{3(x^4+2x-e^x)^{2/3}}$$
   • $$\frac{4x^3+2-e^x}{(x^4+2x-e^x)^{1/3}}$$
   • $$4x^3+2-e^x$$

2. Find $$\frac{d}{dx}\left(\sec(\arcsin(x^2))\right)$$.

   • $$\sec(\arcsin(x^2))\frac{2x}{\sqrt{1-x^4}}$$
   • $$\tan(\arcsin(x^2))\frac{2x}{\sqrt{1-x^4}}$$
   • $$\frac{2x}{\sqrt{1-x^4}}$$
   • $$\sec(\arcsin(x^2))\tan(\arcsin(x^2))\frac{2x}{\sqrt{1-x^4}}$$

3. Find $$\frac{d}{dx}\left(\tan(\sin(4x-1))\right)$$.

   • $$\sec^2(\sin(4x-1))\cos(4x-1)\cdot 4$$
   • $$\sec^2(\sin(4x-1))\cos(4x-1)$$
   • $$\sec(\sin(4x-1))\cos(4x-1)\cdot 4$$
   • $$\cos(4x-1)\cdot 4$$

4. Find $$\frac{d}{dx}\left(6^{5\ln(\operatorname{arcsec}(e^x))}\right)$$.

   • $$5\ln 6\cdot 6^{5\ln(\operatorname{arcsec}(e^x))}\sqrt{e^{2x}-1}$$
   • $$\frac{5\cdot 6^{5\ln(\operatorname{arcsec}(e^x))}}{\sqrt{e^{2x}-1}}$$
   • $$\frac{5\ln 6\cdot 6^{5\ln(\operatorname{arcsec}(e^x))}}{\operatorname{arcsec}(e^x)\sqrt{e^{2x}-1}}$$
   • $$6^{5\ln(\operatorname{arcsec}(e^x))}$$

5. Find $$\frac{dy}{dx}$$ if $$y=\sin x\ln x^2$$.

   • $$\cos x\ln x^2+\sin x\frac{2}{x}$$
   • $$\sin x\frac{2}{x}$$
   • $$\cos x\ln x^2$$
   • $$\cos x+\frac{2}{x}$$

6. Find $$\frac{dy}{dx}$$ using Product Rule if $$y=\frac{\arctan 3x}{e^{-3x^2}}$$.

   • $$e^{-3x^2}\left(\frac{3}{1+9x^2}+6x\arctan 3x\right)$$
   • $$e^{3x^2}\left(\frac{3}{1+9x^2}+6x\arctan 3x\right)$$
   • $$\frac{3}{1+9x^2}$$
   • $$6x\arctan 3x$$

7. Find $$\frac{dy}{dx}$$ if $$y=x^3\sqrt{2x+\cos x}$$.

   • $$3x^2\sqrt{2x+\cos x}+x^3\frac{2+\sin x}{2\sqrt{2x+\cos x}}$$
   • $$3x^2+x^3$$
   • $$3x^2\sqrt{2x+\cos x}+x^3\frac{2-\sin x}{2\sqrt{2x+\cos x}}$$
   • $$3x^2\sqrt{2x+\cos x}$$

8. Find $$\frac{dp}{dx}$$ if $$p=\sec x\cdot\arctan x$$.

   • $$\sec x\tan x\arctan x+\frac{\sec x}{1+x^2}$$
   • $$\sec x\tan x$$
   • $$\sec x\frac{1}{1+x^2}$$
   • $$\sec x\arctan x$$

9. Find $$\frac{d}{dx}\left((x^2+1)^3(3x^2+2x)^2\right)$$.

   • $$(3x^2+2)(30x^3+8x^2-12x+4)$$
   • $$(x^2-11)^2(3x^3+6x^2+6x+1)$$
   • $$\left(x^2+1\right)^2\left(3x^2+2x\right)\left(30x^3+16x^2+12x+4\right)$$
   • $$(x^2+1)^2(30x^3+6x^2+6x+10)$$

10. Evaluate $$y'(x)$$ if $$y=\cos x\sin x\tan x$$.

    • $$\sin x\cos x$$
    • $$2\sin x\cos x$$
    • $$1+(\cos x)^2$$
    • $$\sin x$$