Quiz about Chapter 2 Quiz

Question 1

Which one describe your feeling before taking the quiz?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 2

Find the derivative of

$$f\left(x\right)=3x^2+6\cos x+2^x$$

Accepted Answer

$$6x-6\sin x+2^x\ln2$$

Answer

$$6x+6\sin x+\frac{2^x}{\ln2}$$

Answer

$$6x+6\sin x+2^x\ln2$$

Answer

D.

Question 3

Find the derivative of

$$f\left(x\right)=\sqrt[]{2x}+\frac{1}{4x^2}-\log_3x$$

Accepted Answer

$$\frac{\sqrt[]{2}}{2\sqrt[]{x}}-\frac{1}{2x^3}-\frac{1}{x\ln3}$$

Answer

A.

Answer

$$\frac{\sqrt[]{2}}{2\sqrt[]{x}}+\frac{1}{2x^3}-\frac{1}{x\ln3}$$

Answer

$$\frac{\sqrt[]{2x}}{2}-\frac{1}{2x^3}-\frac{\ln3}{x}$$

Question 4

Find the derivative of

$$f\left(x\right)=x^2\left(e^x+1\right)$$

Accepted Answer

$$x^2e^x+2x\left(e^x+1\right)$$

Answer

$$2x\left(e^x+1\right)-x^2e^x$$

Answer

$$2x\left(e^x+1\right)$$

Answer

D.

Question 5

Find the derivative of $$f\left(x\right)=\frac{x^2+2}{\ln\left(2x\right)}$$

Accepted Answer

$$\frac{2x\ln\left(2x\right)-\frac{\left(x^2+2\right)}{x}}{\left(\ln\left(2x\right)\right)^2}$$

Answer

$$\frac{2x\ln\left(2x\right)-\frac{\left(x^2+2\right)}{2x}}{\left(\ln\left(2x\right)\right)^2}$$

Answer

B.

Answer

$$\frac{\frac{\left(x^2+2\right)}{x}-2x\ln\left(2x\right)}{\left(\ln\left(2x\right)\right)^2}$$

Question 6

Find the derivative of

$$f\left(x\right)=\sin\left(x^2+e^x\right)$$

Accepted Answer

$$\cos\left(x^2+e^x\right)\left(2x+e^x\right)$$

Answer

A.

Answer

$$-\cos\left(x^2+e^x\right)$$

Answer

$$-\cos\left(x^2+e^x\right)\left(2x+e^x\right)$$

Question 7

Find the derivative of

$$f\left(x\right)=3^{2x^2+x}$$

Accepted Answer

$$\left(\ln3\right)\left(4x+1\right)\left(3^{2x^2+x}\right)$$

Answer

$$\left(\ln3\right)\left(3^{2x^2+x}\right)$$

Answer

$$\left(2x^2+x\right)\left(3^{2x^2+x-1}\right)$$

Answer

D.

Question 8

Find the derivative of

$$\ln\left(\frac{\cos^2\left(x\right)}{e^{2x}}\right)$$

Accepted Answer

$$-\frac{2\left(\sin x\right)}{\cos x}-2$$

Answer

$$\frac{2\left(\sin x\right)}{\cos x}-2$$

Answer

$$\frac{e^{2x}}{\cos^2x}$$

Answer

D.

Question 9

Find the derivative of

$$f\left(x\right)=\sin^3\left(3x\right)$$

Accepted Answer

$$9\sin^2\left(3x\right)\cos\left(3x\right)$$

Answer

A.

Answer

$$9\cos^3\left(3x\right)$$

Answer

$$9\sin^2\left(3x\right)$$

Question 10

Find the instantaneous rate of change of

$$f\left(x\right)=\ln\left[\left(x+1\right)^2\right]$$ at $$x=1$$

Accepted Answer

$$1$$

Answer

$$-1$$

Answer

$$2$$

Answer

C.

Question 11

Find the slope of the tangent line of

$$f\left(x\right)=e^{3x}-\cos\left(x^2\right)$$ at $$x=0$$

Accepted Answer

$$3$$

Answer

A.

Answer

$$0$$

Answer

$$2$$

Question 12

Find $$\frac{dy}{dx}$$ of $$\frac{x^2}{4}+9y^2=1$$

Accepted Answer

$$-\frac{x}{36y}$$

Answer

A.

Answer

$$-\frac{x}{2}$$

Answer

$$\frac{x}{36y}$$

Question 13

Find $$\frac{dy}{dx}$$ of $$x^3+y^3=3xy$$

Accepted Answer

$$\frac{y-x^2}{y^2-x}$$

Answer

A.

Answer

$$\frac{y+x^2}{y^2+x}$$

Answer

$$\frac{y+x^2}{y^2-x}$$

Question 14

Find the slopes of the tangent lines to the curve $$5y^2+\sin y=x^2$$ at the point $$\left(0,0\right)$$

Accepted Answer

$$0$$

Answer

A.

Answer

$$1$$

Answer

$$-1$$

Question 15

After the quiz, which one describe you?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

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