Reference no: EM13838094
As we have seen lim h→0 f(x+h) - f(x)/h to find a derivative each time is a long process and often cumbersome. But, there are a few algorithms that work perfectly for finding derivatives. They are the power rule, the product rule, the quotient rule, and the chain rule.
Category 1: Power Rule
Directions: Look at the examples below then answer questions 1&2.
a. f(x) = x3 - 3x + 4
d. f(x) = 5x4
f'(x) = 3x2 - 3f'(x) = 20x3
c. f(x) = 3√x
f'(x) = 3/2√x
d. f(x) = 6/x4
f'(x) = - 24/x5
1. Describe in your own words how to find aderivative using the Power Rule. What must be done to c.) and d.) above before using the power rule to differentiate ?
2. Find the derivative of f(x) = -3x4 - 2√x + 2/x2
Category 2: Product Rule
Directions: Look at the examples below then answer questions 3.
a. f(x)=(x^2+4x-2)(5x-7)
f^' (x)=5(x^2+4x-2)+(2x+4)(5x-7)=5x^2+20x-10+10x^2-14x+20x-28=15x^2+26x-38
SIMPLIFIED ANSWER
b. f(x)=2x√x
f^' (x)=(2x) 1/(2√x)+2(√x)=x/√x+2√x=√x+2√x=3√x
Category 2: Product Rule
Directions: Look at the examples below then answer questions 3.
f(x)=(x^2+4x-2)(5x-7)
f^' (x)=5(x^2+4x-2)+(2x+4)(5x-7)=5x^2+20x-10+10x^2-14x+20x-28=
= 15x^2+26x-38 ← SIMPLIFIED ANSWER
f(x)=2x√x
f^' (x)=(2x) 1/(2√x)+2(√x)=x/√x+2√x=√x+2√x=3√x
↑ RULE ↑ answer ↑SIMPLIFIED
3.)i.) Describe, in your own words, how to find a derivative using the product rule.
ii.)Find the derivative for f(x) = (2x + 3)(5x2 - 3x + 1)
iii.) Explain what steps were taken to change the answer to the simplified form for b.)
Attachment:- MATH260_W2_Lab_Worksheet (1) (1).docx
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