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Differentiation Skills Challenge

Authored by Renuka Rana

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12th Grade

Differentiation Skills Challenge
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20 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find dy/dx for x = 2sin(t), y = 3cos(t)

dy/dx = -2sin(t)

dy/dx = -3tan(t)

dy/dx = -2tan(t)

dy/dx = 2tan(t)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Calculate d/dx(2x^2 + 3x + 1)

4x + 2

3x + 1

2x^2 + 3

4x + 3

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Differentiate y^3 = x^2 + 2xy

dy/dx = (2x)/(3y^2 - 2x)

dy/dx = (2x)/(3y^2 + 2x)

dy/dx = (2x)/(3y^2 + 2y)

dy/dx = (2x)/(3y^2 - 2y)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Apply the chain rule to find dy/dx for y = (2x^2 + 3x)^3

dy/dx = 3(2x^2 + 3x)^2 * (4x - 3)

dy/dx = 3(2x^2 + 3x)^2 * (4x + 3)

dy/dx = 3(2x^2 + 3x)^2 * (2x + 3)

dy/dx = 3(2x^2 + 3x)^2 * (8x + 3)

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the derivative of y = x^2 * e^x using the product rule

y' = 2x*e^x + x^2*e^x

y' = 2x*e^x - x^2*e^x

y' = 2x*e^x + e^x

y' = x^2*e^x - 2x*e^x

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given y = sin(x) / x, find dy/dx using the quotient rule

(cos(x)*x - sin(x)) / x^2

(cos(x)*x + sin(x)) / x^2

(cos(x) - sin(x)) / x^2

(cos(x) + sin(x)) / x^2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Differentiate x^2 + y^2 = 25 implicitly

-x/y

2x + 2y = 0

y/x

x/y

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