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Chain Rule

  • Thread starter oswald
  • Start date
22
0
1. Homework Statement
Finda dw/dt
w=3xy/x²-y²
x=t3
y=e2t

2. Homework Equations
w=(3t3e2t)/(t6-e4t)


3. The Attempt at a Solution
Well,is there anothe way to solve this, instead of dw/dt; like dw/dx * dw/dt + dw/dy * dy/dt ?
1. Homework Statement



2. Homework Equations



3. The Attempt at a Solution
 

Dick

Science Advisor
Homework Helper
26,258
618
Sure. You could just the chain rule as well. You should get the same answer both ways. Just substituting like you did looks to be a little easier.
 
22
0
Chain Rule Exponential and logarithmic

f(x) = ln [ e^ln(x+1) ]
f' = ?
 
32,580
4,310
Simplify it a bit first to make your differentiation easier. What is ln(e^whatever)?
 
22
0
f(x) = ln { e^[ln(x+1)] }

well, i have this answer, but i dont understand
ln [ e^ln(x+1) ] = ln(x+1)

f'(x) = 1/(e^ln(x+1)) * e^ln(x+1) * 1/(x+1) = 1/(x+1)
 
32,580
4,310
The ln and exp functions are inverses of one another, so for any real number u, ln(eu) = u. This means that you can simplify your function before taking its derivative. Then, what you end up differentiating is much simpler.
 

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