Differentiation — Quiz 1

Questions in this quiz (10)

1. What is the average rate of change of $$g(x)=\cos x$$ on $$\left[\frac{\pi}{3},\frac{5\pi}{6}\right]$$?

   • $$\frac{\sqrt3+1}{\pi}$$
   • $$-\frac{\sqrt3+1}{\pi}$$
   • $$-\frac{\sqrt3-1}{\pi}$$
   • $$\frac{\sqrt3-1}{\pi}$$

2. Find $$\frac{dy}{dx}$$ if $$y=8x^{\pi}$$

   • $$8x^{\pi-1}$$
   • $$\pi x^{\pi-1}$$
   • $$8\pi x^{\pi-1}$$
   • $$8\pi x^\pi$$

3. Find $$y'$$ if $$y=\frac{\sqrt{x}+3x^4}{5\sqrt{x}}$$

   • $$\frac{21}{10}x^{5/2}$$
   • $$\frac{1}{10\sqrt{x}}+\frac{12x^3}{5}$$
   • $$\frac{1}{5\sqrt{x}}+\frac{12x^3}{5}$$
   • $$\frac{1}{10x}+12x^3$$

4. What is the equation of the tangent line to $$h(x)=x^3-2x+4$$ at the point $$(1,3)$$?

   • $$y=1(x-1)+3$$
   • $$y=3(x-1)+3$$
   • $$y=5(x-1)+3$$
   • $$y=2(x-1)+3$$

5. Find $$\frac{d}{dx}(\sqrt{\sec x})$$

   • $$\frac{\sec x}{2\sqrt{\sec x}}$$
   • $$\sqrt{\sec x}\tan x$$
   • $$\frac{\tan x}{2\sqrt{\sec x}}$$
   • $$\frac{\sec x\tan x}{2\sqrt{\sec x}}$$

6. Find $$\frac{d}{dx}(\ln(x^2+9))$$

   • $$\frac{2x}{x^2+9}$$
   • $$\frac{x^2+9}{2x}$$
   • $$2x\ln(x^2+9)$$
   • $$\frac{2}{x^2+9}$$

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

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

8. Given $$f$$ is differentiable and the table below:Evaluate $$m'(2)$$ if $$m(x)=(f(x))^2$$.

   • $$8$$
   • $$16$$
   • $$4$$
   • $$32$$

9. Let $$h$$ be differentiable on $$[0,2\pi]$$.If $$p(x)=\cos^2(h(2x))$$, evaluate $$p'\left(\frac{\pi}{2}\right)$$.

   • $$0$$
   • $$2$$
   • $$-2$$
   • $$1$$

10. Find $$\frac{d}{dx}$$ for $$\ln(5x^3+3\cos x)$$.

    • $$\frac{5x^3+3\cos x}{15x^2-3\sin x}$$
    • $$15x^2-3\sin x$$
    • $$\frac{15x^2+3\sin x}{5x^3+3\cos x}$$
    • $$\frac{15x^2-3\sin x}{5x^3+3\cos x}$$