Free Printable Introduction to Power Rule

1.

Hey Sofia and Samantha! Can you help Billie find the derivative of the given equation?
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

2.

Hey Mateo can you help Luciana find the derivative of the following equation?
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

3.

Hey there, math whizzes! Can you help Alejandro differentiate the function y = $\frac{12}{x^2}$ ? Let's see if you can find the right answer!

a)

y' = 24x^-1

b)

y' = -24x^-3

c)

y' = -24x^-1

d)

y' = 6x^-3

4.

Hey there, math wizards! Zafra and Russi are trying to find the derivative of a function, but they need your help! (Hint: you will need to multiply first!)

a)

4x⁸+60x⁶+12x³

b)

12x⁷+36x²

c)

32x⁷+36x²

d)

20x⁶

5.

Hey there, math whizzes! Hurtado, Tomas, and Nicolle are trying to solve the puzzle of finding dy/dx for the function y = 4x³+ 3x + 1. Can you help them out?

a)

dy/dx = 4x² + 3

b)

dy/dx = 4x² + 3x

c)

dy/dx = 12x² + 3x

d)

dy/dx = 12x² + 3

6.

Hey Tomas, Moises, and Silvana Can you tell me what the term 'Derivative' means? Is it the same as:

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

slope of the secant line

7.

Hey Manuela, Victoria, and Esteban! Let's have some fun with calculus! Can you figure out what the derivative of xⁿ is?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

8.

Hey there, math whizzes! Camila, Gabriela, and Isabela are on a quest to find f'(x) when $f\left(x\right)=x^3+x\ +\ 3$

a)

$3x^3+x-10$

b)

$3x^2+1$

c)

$x^2+8$

d)

$4x-6$

9.

Hey Catalina, can you help Sofia find f'(x) when f(x) = 3? Let's see if you can solve this!

a)

0

b)

-6

c)

1

d)

8

10.

Hey there, math whizzes! Can you help Maria Jose find f'(x) when $f\left(x\right)=4x^2-3+\frac{3}{x^2}$ ? Let's see if you can solve this puzzle!

a)

$4x+3+\frac{3}{x^3}$

b)

$2x+1$

c)

$8x-\frac{6}{x^3}$

d)

$8x^2+7-\frac{6}{x^2}$

11.

Hey there, math whizzes! Parra and Luciana are on a quest to find the derivative of the function $f\left(x\right)=x^{-6}$ . Can you help them out? What is $f'\left(x\right)$ in its simplest form?

a)

$-6x^{-7}$

b)

$\frac{-6}{x^7}$

c)

$-6x^{-5}$

d)

$\frac{-6}{x^{-7}}$

12.

Hey there, math wizards! Michael, Billie is on a quest to solve a challenging problem. Can you help her determine the derivative of the function below?

$y\ =\ -5x^4+3x^3-2x^2+9$

What is $\frac{dy}{dx}$ ?

a)

$\frac{dy}{dx}=-5x^3+3x^2-2x$

b)

$\frac{dy}{dx}=-20x^4+9x^3-4x^2+9$

c)

$\frac{dy}{dx}=-20x^3+9x^2-4x$

d)

$\frac{dy}{dx}=-20x^3+9x^2-4x+9$

13.

Hey there, math whizzes! Mr. Solomon is on a quest to uncover the secrets of the function $f\left(x\right)=-3x^2+6x-4$ . Can you help him determine the derivative $f'\left(x\right).$ ?

a)

$-3x+6$

b)

$-6x+2$

c)

$-6x^2+6$

d)

$-6x+6$

14.

Hey Russi! Imagine you're on a math adventure with your friend Mateo. Can you help him find the instantaneous rate of change of the function $f\left(x\right)=5x^2-3x$ at the magical point where x = 2? What do you think it is?

(a)

15.

Hey there, math whizzes! Can you help ( sound your name) find the derivative of the following equation?

f(x) = x⁴ + 4x³- 2x²

a)

f'(x) = x³ + x²- x

b)

f'(x) = 4x³ + 12x²+ 4x

c)

f'(x) = 4x + 12x - 4x

d)

f'(x) = 4x³ + 12x²- 4x

16.

Hey there, math whizzes! Camila and Esteban are on a quest to find the derivative of the magical equation
$f\left(x\right)=\frac{1}{x^2}$ . Can you help them out? Hint: Rewrite first!

a)

$f'\left(x\right)=\frac{1}{2x}$

b)

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

c)

$f'\left(x\right)=2x$

d)

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

17.

Find the derivative of the magical equation below:

g(x) = 1 - x²

a)

g'(x) = 1 - 2x

b)

g'(x) = -2x

c)

g'(x) = -2

d)

g'(x) = -1

18.

Ava and Mason are having a math challenge! Can you help them find the slope of the tangent line to the function y = 4x⁴ - 7x³ + 0.5x² - 9 at the point where x=1?

a)

16x³ - 21x² + x

b)

6

c)

16x³ - 21x² + 0.5x - 9

d)

-4

19.

When we "take the derivative" of a function, what exciting thing are we discovering?

a)

What's a derivative, anyway?

b)

The rate at which our struggles in Calculus are skyrocketing!

c)

The slope of the secant line, right?

d)

The slope of the tangent line, of course!

20.

Find the derivative of the function: $f\left(x\right)=-\frac{10}{3}$

a)

$f'\left(x\right)=-\frac{10}{3x}$

b)

$f'\left(x\right)=-\frac{10x}{3}$

c)

$f'\left(x\right)=\frac{10x}{3}$

d)

$f'\left(x\right)=0$

21.

Find the derivative of $y=\frac{12}{x^2}$

a)

^{$y'=\frac{24}{x}$} - Great job, you got it!

b)

^{$y'=-\frac{24}{x^3}$} - Oops! Not quite right.

c)

^{$y'=-\frac{24}{x}$} - Close, but not the answer we're looking for!

d)

^{$y'=\frac{6}{x^3}$} - Not this one either!

22.

find the derivative of the function: $f\left(x\right)=\sqrt{x^5}$

a)

$f'\left(x\right)=\frac{5}{2\sqrt{x^3}}$

b)

$f'\left(x\right)=\frac{5\sqrt{x^3}}{2}$

c)

$f'\left(x\right)=-\frac{5}{2\sqrt{x^3}}$

d)

$f'\left(x\right)=-\frac{5\sqrt{x^3}}{2}$

Introduction to Power Rule

Total questions: 22

Worksheet time: 27mins

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