Free Printable 미적분 Unit 2 Test Review 2.1-3.1

1.

거듭제곱 법칙을 사용하여 다음 도함수를 결정합니다:

Use the Power Rule to determine the following derivative: $f\left(x\right)=3x^6-x^3$

a)

$f'(x)=18x^5-3x^2$

b)

$f'(x)=18x^6-3x^2$

c)

$f'(x)=18x^4-3x$

d)

$f'(x)=6x^5-3x^3$

2.

체인 규칙을 사용하여 다음 함수의 도함수를 찾습니다:

Use the Chain Rule to find the derivative of the following function: $f\left(x\right)=\sin\left(\sin\left(x\right)\right)$

a)

$f'(x)=\cos(x)\cdot\sin(\sin(x))$

b)

$f'(x)=-\cos(\sin(x))\cdot\sin(x)$

c)

$f'\left(x\right)=\cos\left(\sin\left(x\right)\right)\cdot\cos\left(x\right)$

d)

$f'(x)=\sin(\sin(x))\cdot\sin(x)$

3.

곱셈 규칙을 사용하여 다음 함수의 미분을 구합니다:

Use the Product Rule to find the derivative of the following function: $f\left(x\right)=e^x\left(2x-5\right)$

a)

$f'(x)=e^x(2x-5)$

b)

$f'(x)=e^x(2x-2)$

c)

$f'(x)=e^x(2x-4)$

d)

$f'(x)=e^x(2x-3)$

4.

몫의 법칙을 사용하여 다음 함수의 도함수를 구합니다:

Use the quotient rule to find the derivative of the following function: $f\left(x\right)=\frac{\sin\left(x\right)}{3\sqrt{\ x}}$

a)

$\frac{2x\cos\left(x\right)-\sin\left(x\right)}{6x^{\frac{3}{2}}}$

b)

$\frac{2x\cos\left(x\right)-\sin\left(x\right)}{9\sqrt{\ x}}$

c)

$\frac{3\cos\left(x\right)\sqrt{\ x}}{9x}-\frac{3\sin\left(x\right)}{2\sqrt{\ x}}$

d)

$3\cos\left(x\right)\sqrt{\ x}+\frac{3\sin\left(x\right)}{2\sqrt{\ x}}$

5.

곱셈 규칙을 사용하여 다음 함수의 미분을 구합니다:

Use the Product Rule to find the derivative of the following function: $f\left(x\right)=\left(3\sqrt{\ x}\right)\sin\left(x\right)$

a)

$\frac{2x\cos\left(x\right)-\sin\left(x\right)}{6x^{\frac{3}{2}}}$

b)

$\frac{2x\cos\left(x\right)-\sin\left(x\right)}{9\sqrt{\ x}}$

c)

$\frac{3\cos\left(x\right)\sqrt{\ x}}{9x}-\frac{3\sin\left(x\right)}{2\sqrt{\ x}}$

d)

$3\cos\left(x\right)\sqrt{\ x}+\frac{3\sin\left(x\right)}{2\sqrt{\ x}}$

6.

체인 규칙을 사용하여 다음 함수의 도함수를 찾습니다:

Use the Chain Rule to find the derivative of the following function: $f\left(x\right)=\cos\left(3x^2\right)$

a)

$f'(x)=-6x\sin(3x^2)$

b)

$f'(x)=6x\cos(3x^2)$

c)

$f'(x)=-3x\sin(3x^2)$

d)

$f'(x)=3x\cos(3x^2)$

7.

곱셈 규칙을 사용하여 다음 함수의 미분을 구합니다:

Use the Product Rule to find the derivative of the following function: $f\left(x\right)=x^2\ln(x)$

a)

$f'(x)=2x\ln(x)+x$

b)

$f'(x)=x^2\ln(x)+2x$

c)

$f'(x)=2x\ln(x)-x$

d)

$f'(x)=x^2\ln(x)-2x$

8.

몫의 법칙을 사용하여 다음 함수의 도함수를 구합니다:

Use the Quotient Rule to find the derivative of the following function: $f\left(x\right)=\frac{x^3}{e^x}$

a)

$f'(x)=\frac{3x^2e^x-x^3e^x}{(e^x)^2}$

b)

$f'(x)=\frac{3x^2e^x+x^3e^x}{(e^x)^2}$

c)

$f'(x)=\frac{x^3e^x-3x^2e^x}{(e^x)^2}$

d)

$f'(x)=\frac{x^3e^x+3x^2e^x}{(e^x)^2}$

9.

다음 함수의 2차 도함수는 무엇입니까?

What is the second derivative of the following function: $f\left(x\right)=\tan\left(x\right)$

a)

$f''(x)=2\sec^2(x)\tan(x)$

b)

$f''(x)=\sec^2(x)$

c)

$f''(x)=2\tan^2(x)$

d)

$f''(x)=2\sec^4(x)$

10.

다음 함수의 3차 도함수는 무엇입니까?

What is the third derivative of the following function: $y=e^{x^2+2}$

a)

$\frac{d^3y}{dx^3}=4xe^{\left(x^2+2\right)}\left(2x^2+3\right)$

b)

$\frac{d^3y}{dx^3}=4x^3e^{\left(x^2+2\right)}$

c)

$\frac{d^3y}{dx^3}=e^{\left(x^2+2\right)\left(2x+3\right)}$

d)

Not doing it this way, takes too long. Mr. Clarke will show me the shortcut shortly..

미적분 Unit 2 Test Review 2.1-3.1

Total questions: 10

Worksheet time: 14mins

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