Solution-Finding derivatives, As we have seen lim h?0 | Quick Homework Help

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)(5×2 – 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