Differentiation — Quiz 2

Questions in this quiz (10)

1. If $$y=\sin(2x+5)$$, find $$\frac{dy}{dx}$$.

   • $$2\sin(2x+5)$$
   • $$2\cos(2x+5)$$
   • $$-2\sin(2x+5)$$
   • $$\cos(2x+5)$$

2. If $$y=(x+3)\ln(x+2)$$, find $$\frac{dy}{dx}$$.

   • $$\ln(x+3)+\frac{x+3}{x+2}$$
   • $$\frac{1}{x+2}+\frac{x+3}{x+2}$$
   • $$\ln(x+2)+\frac{x+3}{x+2}$$
   • $$\ln(x+2)+\frac{x+2}{x+3}$$

3. If $$f(x)=1+\cos(4x)$$, find $$f'(x)$$.

   • $$-4\cos(4x)$$
   • $$-\sin(4x)$$
   • $$4\sin(4x)$$
   • $$-4\sin(4x)$$

4. If $$y=\sin^{-1}(2x)+\sqrt{1-4x^2}$$, find $$\frac{dy}{dx}$$.

   • $$\frac{4x-2}{\sqrt{1-4x^2}}$$
   • $$\frac{2-4x}{1-4x^2}$$
   • $$\frac{2+4x}{\sqrt{1-4x^2}}$$
   • $$\frac{2-4x}{\sqrt{1-4x^2}}$$

5. If $$u=\ln\sqrt{x^2+4x+5}$$, find $$\frac{du}{dx}$$.

   • $$\frac{1}{x^2+4x+5}$$
   • $$\frac{2x+4}{x^2+4x+5}$$
   • $$\frac{x+2}{x^2+4x+5}$$
   • $$\frac{x+2}{x^2+4x}$$

6. If $$f(x)=e^x(\sin x+\cos x)$$, find $$f'(x)$$.

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

7. Let $$y=3u^3-2u^2+4u-1$$ and $$u=x^2+2x$$. Find $$\frac{dy}{dx}$$.

   • $$(9x^4+36x^3+28x^2-8x+4)(2x+2)$$
   • $$(9x^4+36x^3+32x^2-8x+4)(2x+2)$$
   • $$18x^4+72x^3+64x^2-16x+8$$
   • $$2x(9x^4+36x^3+32x^2-8x+4)$$

8. If $$y=\cos(ax+b)$$, with $$a$$ and $$b$$ constants, find $$\frac{dy}{dx}$$.

   • $$\sin(ax+b)$$
   • $$-a\cos(ax+b)$$
   • $$a\sin(ax+b)$$
   • $$-a\sin(ax+b)$$

9. If $$g(x)=b\sin(kx)$$ with $$b$$ and $$k$$ constants, find $$g'(x)$$ and $$g''(x)$$.

   • $$g'(x)=bk\cos(kx)$$, $$g''(x)=-bk^2\sin(kx)$$
   • $$g'(x)=bk^2\cos(kx),\ g''(x)=-b\sin(kx)$$
   • $$g'(x)=bk\sin(kx),\ g''(x)=bk^2\cos(kx)$$
   • $$g'(x)=b\cos(kx),\ g''(x)=-bk\sin(kx)$$

10. If $$y=\ln(ax+b)$$, where $$a$$ and $$b$$ are constants, find $$\frac{dy}{dx}$$.

    • $$\frac{b}{ax+b}$$
    • $$\frac{a}{x+b}$$
    • $$\frac{a}{ax+b}$$
    • $$\frac{1}{ax+b}$$