Mastering Derivatives and Functions

Mastering Derivatives and Functions

12th Grade

16 Qs

quiz-placeholder

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Mastering Derivatives and Functions

Mastering Derivatives and Functions

Assessment

Quiz

Others

12th Grade

Practice Problem

Hard

Created by

Nipun Mattu

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16 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the derivative of f(x) = (3x^2 + 2x)^5 using the chain rule?

f'(x) = 15(3x^2 + 2x)^4 * (6x)

f'(x) = 5(3x^2 + 2x)^4 * (6x + 2)

f'(x) = 5(3x^2 + 2x)^4 * (3x + 1)

f'(x) = 5(3x^2 + 2x)^3 * (6x + 2)

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

If y = sin(2x^3), find dy/dx using the chain rule.

dy/dx = 6x^2 * cos(2x^3)

dy/dx = 12x^3 * cos(2x^3)

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

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

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Determine if the function f(x) = x^3 - 3x is one-to-one.

Yes

It is one-to-one

No

It has a unique inverse

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the derivative of the implicit function defined by x^2 + y^2 = 25.

dy/dx = -y/x

dy/dx = x/y

dy/dx = 2x + 2y

dy/dx = -x/y

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Using implicit differentiation, find dy/dx for the equation x^2y + y^3 = 6.

2x^2y / (y^2 + 6)

3y^2 / (x^2 + 2xy)

-2xy / (x^2 + 3y^2)

-y^3 / (2x + 3y)

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of g(t) = e^(3t^2) using the chain rule?

g'(t) = 6t * e^(3t^2)

g'(t) = 6 * e^(3t^2)

g'(t) = 9t^2 * e^(3t)

g'(t) = 3t * e^(3t^2)

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Is the function f(x) = ln(x) + x^2 one-to-one? Justify your answer.

No, the function f(x) = ln(x) + x^2 is not one-to-one.

Yes, the function f(x) = ln(x) + x^2 is one-to-one only for x > 0.

The function f(x) = ln(x) + x^2 is one-to-one because it is a polynomial.

Yes, the function f(x) = ln(x) + x^2 is one-to-one.

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