9th
-
12th
grade

Mathematics

73%

accuracy

plays

Kristin D'Emanuele

3 years

Mathematics

9th -

12thgrade

Calculus Derivative Rules Practice

Kristin D'Emanuele

33
plays

11 questions

Show Answers

See Preview

1. Multiple Choice
3 minutes
1 pt
If
$If\ y=\left(x^3+1\right)^2,\ then\ \frac{dy}{dx}=$
$\left(3x^2\right)^2$
$2\left(x^3+1\right)$
$2\left(3x^2+1\right)$
$3x^2\left(x^3+1\right)$
$6x^2\left(x^3+1\right)$
2. Multiple Choice
3 minutes
1 pt
$If\ g\left(x\right)=\frac{x-2}{x+2},\ then\ g'\left(2\right)=$
1
-1
1/4
-1/4
0
3. Multiple Choice
3 minutes
1 pt
Find the derivative of the following:
$\sqrt{x}-\frac{1}{x^{\frac{4}{3}}}$
$\frac{1}{2}x^{-\frac{1}{2}}-x^{-\frac{4}{3}}$
$\frac{1}{2}x^{-\frac{1}{2}}+\frac{4}{3}x^{-\frac{7}{3}}$
$\frac{1}{2}x^{-\frac{1}{2}}-\frac{4}{3}x^{-\frac{1}{3}}$
$-\frac{1}{2}x^{-\frac{1}{2}}+\frac{4}{3}x^{-\frac{7}{3}}$
$-\frac{1}{2}x^{-\frac{1}{2}}-\frac{4}{3}x^{-\frac{1}{3}}$
4. Multiple Choice
3 minutes
1 pt
Find f'(2) if
$f\left(x\right)=\frac{x^2-2}{x-1}$
-2
1/6
1/2
2
6
5. Multiple Choice
3 minutes
1 pt
Let f be the function defined below. Which of the following is an equation of the line tangent to the graph of f at the point where x = -1?
$f\left(x\right)=4x^3-5x+3$
y = -7x - 3
y = 7x + 7
y = 7x + 11
y = -5x - 1
y = -5x - 5
6. Multiple Choice
3 minutes
1 pt
$If\ y=\frac{3}{4+x^2},\ then\ \frac{dy}{dx}=$
$\frac{3}{2x}$
$\frac{3x}{\left(1+x^2\right)^2}$
$\frac{6x}{\left(4+x^2\right)^2}$
$-\frac{6x}{\left(4+x^2\right)^2}$
$-\frac{3}{\left(4+x^2\right)^2}$
7. Multiple Choice
3 minutes
1 pt
If the line tangent to the graph of the function f at the point (1,7) passes through the point (-2, -2), then f'(1) =
-5
1
3
7
undefined
8. Multiple Choice
3 minutes
1 pt
Let f be a differentiable function with f(2) = 3 and f'(2) = -5, and let g be a function defined by g(x) = x ^.f(x). Which of the following is an equation of the line tangent to the graph of g at the point where x = 2?
$y=3x$
$y-3=-5\left(x-2\right)$
$y-6=-5\left(x-2\right)$
$y-6=-7\left(x-2\right)$
$y-6=-10\left(x-2\right)$
9. Multiple Choice
3 minutes
1 pt
If g'(-4) = 2 and h'(-4) = 3, find f'(-4) for
$f\left(x\right)=4g\left(x\right)-6h\left(x\right)+3$
29
-10
26
-7
1
10. Multiple Choice
3 minutes
1 pt
$If\ y=5x^3-6x^2+4,\ find\ \frac{\text{d}^2y}{\text{d}x^2}$
30x - 12
12x - 20
12x - 30
20x - 12
$15x^2-12x$
11. Multiple Choice
3 minutes
1 pt
$If\ y=3x^2+8x+4x^{-3},\ find\ \ y''\left(1\right)$
-42
2
15
54
64
Answer choices
Tags
Answer choices
Tags
Explore all questions with a free account
Already have an account?

Calculus Derivative Rules Practice

9th - 12thgrade

Mathematics

Mathematics

9th -

12thgrade

Calculus Derivative Rules Practice

33 plays

11 questions

Introducing new Paper mode

9th
-
12th
grade

33
plays