disagreed with her result. What did she get right? What did she get wrong? Correct her work. y' = h'(x)e-4f(x) +h(x)e-4f(x) (-4) After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(r)e-4f(x) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method. h(a) 2. Two students are trying to find the derivative y' of y = e(K) ³. h(x) • Otto tried using the chain rule, letting the interior function be u = k(x) • Naomi tried using the chain rule, letting the interior function be u = h(x) k(x) Are Otto's and Naomi's methods both acceptable? Try both methods. 3. During Exam 2, some students forgot the formula for the quotient rule. However, Alexander was able to figure it out again using other derivative rules and techniques. Find the quotient rule formula using the method he came up with below. Alexander rewrote as a product (ƒ(a) · (g(x))−¹1)' to derive the quotient rule. g(x) 4. Derive Use your formula to find [(tan 4x)]². Check your solution by finding the derivative using an alternative method. formula for [ƒ(9(h(x)))]. a 5. Find y' if y= two different ways. 6. Confirm your solutions to problems 1, 2, 3, 5 above using logarithmic differentiation. x²+4
disagreed with her result. What did she get right? What did she get wrong? Correct her work. y' = h'(x)e-4f(x) +h(x)e-4f(x) (-4) After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(r)e-4f(x) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method. h(a) 2. Two students are trying to find the derivative y' of y = e(K) ³. h(x) • Otto tried using the chain rule, letting the interior function be u = k(x) • Naomi tried using the chain rule, letting the interior function be u = h(x) k(x) Are Otto's and Naomi's methods both acceptable? Try both methods. 3. During Exam 2, some students forgot the formula for the quotient rule. However, Alexander was able to figure it out again using other derivative rules and techniques. Find the quotient rule formula using the method he came up with below. Alexander rewrote as a product (ƒ(a) · (g(x))−¹1)' to derive the quotient rule. g(x) 4. Derive Use your formula to find [(tan 4x)]². Check your solution by finding the derivative using an alternative method. formula for [ƒ(9(h(x)))]. a 5. Find y' if y= two different ways. 6. Confirm your solutions to problems 1, 2, 3, 5 above using logarithmic differentiation. x²+4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please do 6.
![1. Candace tried to find the derivative of the function y = h(x)e-4f(x) but her group members
disagreed with her result. What did she get right? What did she get wrong? Correct her
work.
-4f(x) (-4)
y' = h'(x)e-4f(x) +h(x)e¯
After figuring out her error, Candace attempted to check her solution by rearranging the right
side of the equation y = h(r)e-4f(x) into a fraction and using the quotient rule to differentiate.
Verify the correct solution using this method.
(2)) ³.
2. Two students are trying to find the derivative y' of y = e
h(z)
k(x)
• Otto tried using the chain rule, letting the interior function be u =
h(x)
k(x).
• Naomi tried using the chain rule, letting the interior function be u =
(h()) ³.
Are Otto's and Naomi's methods both acceptable? Try both methods.
3. During Exam 2, some students forgot the formula for the quotient rule. However, Alexander
was able to figure it out again using other derivative rules and techniques. Find the quotient
rule formula using the method he came up
below.
Alexander rewrote f(x) as a product (ƒ(x) · (g(x))−¹)' to derive the quotient rule.
g(x)
4.
Derive a formula for [f(g(h(x)))]. Use your formula to find [(tan 4x)]². Check your
solution by finding the derivative using an alternative method.
5. Find y' if y= 25 two different ways.
6. Confirm your solutions to problems 1, 2, 3, 5 above using logarithmic differentiation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93724627-c7b6-406b-9a00-d0dcd2c570ce%2Ff030109e-3153-4e2d-ab82-b916d5c5c9ca%2F1si0wvr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Candace tried to find the derivative of the function y = h(x)e-4f(x) but her group members
disagreed with her result. What did she get right? What did she get wrong? Correct her
work.
-4f(x) (-4)
y' = h'(x)e-4f(x) +h(x)e¯
After figuring out her error, Candace attempted to check her solution by rearranging the right
side of the equation y = h(r)e-4f(x) into a fraction and using the quotient rule to differentiate.
Verify the correct solution using this method.
(2)) ³.
2. Two students are trying to find the derivative y' of y = e
h(z)
k(x)
• Otto tried using the chain rule, letting the interior function be u =
h(x)
k(x).
• Naomi tried using the chain rule, letting the interior function be u =
(h()) ³.
Are Otto's and Naomi's methods both acceptable? Try both methods.
3. During Exam 2, some students forgot the formula for the quotient rule. However, Alexander
was able to figure it out again using other derivative rules and techniques. Find the quotient
rule formula using the method he came up
below.
Alexander rewrote f(x) as a product (ƒ(x) · (g(x))−¹)' to derive the quotient rule.
g(x)
4.
Derive a formula for [f(g(h(x)))]. Use your formula to find [(tan 4x)]². Check your
solution by finding the derivative using an alternative method.
5. Find y' if y= 25 two different ways.
6. Confirm your solutions to problems 1, 2, 3, 5 above using logarithmic differentiation.
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