Quiz about Защита темы 2 (Производная)

Question 1

$$\left(4x^3\right)$$

Accepted Answer

$$12x^2$$

Answer

$$4x^2$$

Answer

$$3x^2$$

Answer

$$16x^4$$

Question 2

$$\left(\frac{5}{x^2}\right)$$

Accepted Answer

$$-\frac{10}{x^3}$$

Answer

$$-\frac{10}{x}$$

Answer

$$\frac{10}{x^3}$$

Answer

$$-\frac{10}{x^4}$$

Question 3

$$\left(e^{x^3}\right)$$

Accepted Answer

$$3x^2e^{x^3}$$

Answer

$$e^{3x^2}$$

Answer

$$3x^2+e^{x^3}$$

Answer

$$x^3e^{x^3-1}$$

Question 4

$$\left(\arcsin4x\right)$$

Accepted Answer

$$\frac{4}{\sqrt{1-16x^2}}$$

Answer

$$\frac{4}{\sqrt{1+16x^2}}$$

Answer

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

Answer

$$\frac{1}{\sqrt{1-16x^2}}$$

Question 5

$$\left(\sin\frac{1}{x}\right)$$

Accepted Answer

$$-\frac{\cos\frac{1}{x}}{x^2}$$

Answer

$$\cos\frac{1}{x^2}$$

Answer

$$\frac{\cos\frac{1}{x}}{x}$$

Answer

$$\cos\left(-\frac{1}{x^2}\right)$$

Question 6

$$\left(\frac{\sqrt{x^3}}{4}\right)$$

Accepted Answer

$$\frac{3\sqrt{x}}{8}$$

Answer

$$\frac{\sqrt{x\ }}{12}$$

Answer

$$\frac{3\sqrt{x}}{16}$$

Answer

$$\frac{3}{4\sqrt{x}}$$

Answer

$$\frac{3}{8\sqrt{x}}$$

Question 7

$$y=\ln x,\ \ \ y$$

Accepted Answer

$$-\frac{1}{x^2}$$

Answer

$$\frac{1}{x^2}$$

Answer

$$\frac{1}{x}$$

Answer

$$-\frac{1}{x}$$

Question 8

$$\left(\cos3x\right)$$

Accepted Answer

$$-9\cos3x$$

Answer

$$-\cos3x$$

Answer

$$\sin3x$$

Answer

$$9\sin3x$$

Answer

$$-3\sin3x$$

Question 9

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

Accepted Answer

$$-2\cos x\sin x$$

Answer

$$2\cos x\sin x$$

Answer

$$2\cos x$$

Answer

$$2\sin x$$

Answer

$$-2\sin x$$

Question 10

$$\left(\ln\sin x\right)$$

Accepted Answer

$$	an x$$

Answer

$$\cot x$$

Answer

$$\frac{1}{\sin x}$$

Answer

$$-\frac{1}{\sin x}$$

Question 11

$$\left(\ln^2x\right)$$

Accepted Answer

$$\frac{2\ln x}{x}$$

Answer

$$\frac{1}{x^2}$$

Answer

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

Answer

$$2\ln x$$

Question 12

$$\left(e^xx^2\right)$$

Accepted Answer

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

Answer

$$e^x2x$$

Answer

$$e^x+2x$$

Answer

$$e^x2x+e^x$$

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