Georgia Gwinett College Derivatives Problems Calculus Worksheet

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georgia gwinett college

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Hand In Problems 4 Name_____________________________ Instructions: Each short answer question is worth 10 points. You must show all Algebra and Calculus work. You may not skip any steps. Be sure to write all formulas that you use. Answer all word problems in complete sentences using units. You are on your honor to only use your notes, the textbook, and your graphing calculator but no outside resources. 1. Compute the derivatives using the values in the table below. β„Ž(π‘₯) = π‘₯ 2 𝑓(π‘₯) + 16π‘₯ 5 𝑔(π‘₯) , find β„Žβ€²(3) 2. Use the table to answer the questions that follow. 𝝅 𝝅 x πŸ‘ 𝟐 4 -2 𝑓(π‘₯) 10 4 𝑓 ’(π‘₯) 2 6 𝑔(π‘₯) 4 5 𝑔 ’(π‘₯) 𝑔(π‘₯) πœ‹ If β„Ž(π‘₯) = sin(π‘₯) 𝑔(π‘₯) + tan(π‘₯), find β„Žβ€™ ( 3 ). 𝝅 πŸ’ 3 -5 2 6 𝝅 πŸ” 5 3 4 7
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Explanation & Answer

I solved both problems, please look on them.I tried to double-check but had not much time. The formulas are definitely correct.docx and pdf files are identical

Find the derivative using rules:
β„Žβ€² (π‘₯) = 2π‘₯𝑓(π‘₯) + π‘₯ 2 𝑓 β€² (π‘₯) + 16 βˆ™

5π‘₯ 4 𝑔(π‘₯) βˆ’ π‘₯ 5 𝑔′ (π‘₯)
(𝑔(π‘₯))

2

.

This way
β„Žβ€² (3) = 2 βˆ™ 3 βˆ™ 𝑓(3) + 32 βˆ™ 𝑓 β€² (3) + 16 βˆ™

5 βˆ™ 34 𝑔(3) βˆ’ 35 βˆ™ 𝑔′ (3)
(𝑔(3))

2

.

Substitut...


Anonymous
I was struggling with this subject, and this helped me a ton!

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