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Calculus 1 Answer

This document provides a basic derivatives practice worksheet. It includes rewriting functions, finding derivatives using applicable rules like the power, constant multiple, sum and difference rules, and simplifying without negative exponents. Students are asked to complete the worksheet for homework and the solutions will be reviewed in class next week.

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Phil Harold Nera
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54 views2 pages

Calculus 1 Answer

This document provides a basic derivatives practice worksheet. It includes rewriting functions, finding derivatives using applicable rules like the power, constant multiple, sum and difference rules, and simplifying without negative exponents. Students are asked to complete the worksheet for homework and the solutions will be reviewed in class next week.

Uploaded by

Phil Harold Nera
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Basic Derivatives Practice Worksheet

Try your best on this and finish it for homework. We will go over the
solutions and I will check for completeness next week.
Rewrite each function, differentiate, and then simplify (no negative exponents!)

f(x) = 𝟐𝒙𝟑
𝟓 𝒅 𝟓𝒙−𝟑 𝟏𝟓
= −
𝒅𝒙 𝟐
𝟐𝒙𝟒

f(x) = (𝟐𝒙)𝟑
𝟓 𝒅 𝟓𝒙−𝟑 𝟏𝟓
= −
𝒅𝒙 𝟖
𝟖𝒙𝟒

f(x) = 𝟑𝒙−𝟐
𝟕 𝒅 𝟕𝒙𝟐 𝟏𝟒𝒙
=
𝒅𝒙 𝟑
𝟑

f(x) = √𝒙
𝟔
𝒅 𝟏 𝟏
= 𝒙𝟔
𝒅𝒙 𝟓
𝟔𝒙𝟔

𝟏
f(x) = 𝒙𝟐 + 𝒙𝟑
𝟏 𝒅
= 𝒙−𝟐 + 𝒙−𝟑 𝟐 𝟑
𝒅𝒙 − 𝟑
− 𝟒
𝒙 𝒙

𝟐 𝟑 𝒅 𝟏 𝟐 𝟔
f(x) = 𝟑
√𝒙
−
𝒙𝟐 = 2𝒙−𝟑 − 𝟑𝒙−𝟐 − 𝟒−
𝒅𝒙 𝒙𝟑
𝟑𝒙𝟑

y = 𝑥 2 − 4 (1,3) y = mx+b
y'=2x -3= 2(1)+b
=2 b = -5
y= 2x-5

y = √𝑥 (4,2) y = mx+b
1
y'=𝑥 2 2= 1/2(2)+b
1
1 −
= 𝑥 2 b=0
2
1 𝟏
= y= 𝒙
2 𝟐

1
y = 𝑥 −2 (1,1) y = mx+b
3
1
y'=− 𝑥 −2 1= -1/2(1)+b
2
=-1/2 b = 3/2
𝟏 𝟑
y= − 𝐱+
𝟐 𝟐
The Constant Rule The Power Rule
If n is a rational number, then the function f(x) = xn
The derivative of a constant function is zero. is differentiable and…

d dxn nx n 1

c 0
dx dx

The Constant Multiple Rule The Sum and Difference Rules


If f is a differentiable function and c is a real The sum (or difference) of two differentiable
d functions, f and g, is differentiable and…
number, then c·f is differentiable and… d
'
cfx ( ) cf ( )x f ( )x g x( ) f '( )x g x'( )
dx
dx

Use an applicable rule to find each derivative.


Answer:
1. 5𝑥 4 - 6𝑥 2 + 7
2. 6x + 2
3. 32t +70
2
4. -
𝑥2
1 1 2
5.
√𝑥 11. 4 − 3 + 5
𝑥 5𝑥 5 4𝑥 4 3𝑥 3
8𝑥 14
6. 12. 𝑥
5 5
3 6
7. − 13. 2𝑥 +
2 𝑥3
1 2
8. − 5 14. 2𝑠 − 1
− 3𝑠 3
3𝑥 3
2 2 1
9. 3𝑥 − 4 15. 1 − 2
3 2 3𝑇 3 3𝑇 3
10. -2𝑥 + 9𝑥 − 2 2
16. −45𝑥 + 36𝑥
𝑥 3 −8
17.
𝑥3
2𝑥 2 −1
18.
𝑥2

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