
Mastering Derivatives and Functions
Authored by Nipun Mattu
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12th Grade

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16 questions
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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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