SOLUTION: Hi, can someone help me with this question please? I'm trying hard to put the formula the correct way but I'm not sure
w(x)=(e^x-11 lnx+340x^5)/(7x^3-32e^x+5 lnx )
What
Algebra.Com
Question 1201323: Hi, can someone help me with this question please? I'm trying hard to put the formula the correct way but I'm not sure
w(x)=(e^x-11 lnx+340x^5)/(7x^3-32e^x+5 lnx )
What's the rule and what are three steps that can be applied when differentiating?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
Whenever dealing with complicated formulas, it helps to break things up into smaller pieces.
 = \frac{f(\text{x})}{g(\text{x})})
where
 = e^{\text{x}}-11\ln(\text{x})+340\text{x}^5)
 = 7\text{x}^3-32e^{\text{x}}+5\ln(\text{x}))
We'll need the derivatives of the functions f(x) and g(x) separately.
 = e^{\text{x}}-\frac{11}{\text{x}}+1700\text{x}^4)
 = 21\text{x}^2-32e^{\text{x}}+\frac{5}{\text{x}})
Let me know if you need me to go over the derivative rules.
I'll rewrite each fraction of the form a/b into ab^(-1)
 = e^{\text{x}}-11\text{x}^{-1}+1700\text{x}^4)
 = 21\text{x}^2-32e^{\text{x}}+5\text{x}^{-1})
Use the quotient rule to apply the derivative to w(x)
 = \frac{f'(\text{x})g(\text{x}) - f(\text{x})g'(\text{x})}{(g(\text{x}))^2})
 = \frac{(e^{\text{x}}-11\text{x}^{-1}+1700\text{x}^4)(7\text{x}^3-32e^{\text{x}}+5\ln(\text{x}))-(e^{\text{x}}-11\ln(\text{x})+340\text{x}^5)(21\text{x}^2-32e^{\text{x}}+5\text{x}^{-1})}{(7\text{x}^3-32e^{\text{x}}+5\ln(\text{x}))^2})
Things spiral out of hand by the third step.
You can optionally expand things out and combine like terms.
But it's probably better to leave it as it is.
RELATED QUESTIONS
If L = 6.1 10^30 W and
F = 5.3 10^(10) W m^(-2),
find d in the equation d =... (answered by greenestamps)
I am having a hard time with this one question that I have to do for homework, so someone (answered by Alan3354)
Hello, Can someone show me how to draw a tree diagram, I am really trying but I having a... (answered by ewatrrr)
I need to simplifi this rational expression. The next step I think is to cancel out... (answered by kietra)
A problem on my math homework really gave me a hard time trying to understand it because... (answered by josgarithmetic,stanbon)
I did not find any solvers to help me with trying to solve this problem , can someone... (answered by alvinjohnburgos)
Okay, I am in a basic math class at the Art Institute online. I do not want the answer... (answered by Alan3354)
I am trying to solve the following equations but I am having trouble.
1.... (answered by jim_thompson5910)
Hello! Please help me with this question:
There are 10 students with different designs (answered by greenestamps,ikleyn,ewatrrr)