ECN4371Rulesofdifferentiation

ECN4371Rulesofdifferentiation - = dgh + gdh dx dx dx...

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ECN437 Peter J. Wilcoxen Economics and Public Administration The Maxwell School Syracuse University Rules of Differentiation 1. Constants 2. Powers Example: Example: If f(x) = k,where k is a constant, then df = 0 dx f(x)=3 df=0 dx If f(x) = xn, then df = nxn 1 dx f(x)=x4 df = 4ξ3 dx f(x)=x df=1 dx Example: 3. Sums and Differences Iff(x)=g(x)±h(x),then df =δγ ±δη dx dx dx f(x)=3x4 32x df = 1 2ξ3 - 3 2 dx 4. Products 5. Quotients Example: Example: If f(x) = g(x)h(x), then df
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Unformatted text preview: = dgh + gdh dx dx dx f(x)=x2(x 1) df = 2(-129 +2 dx Iff(x)=g(x),then df = 1 - h(x) dx h2 dx dx f(x)= x2 df = 1 2(7 +29 -2 (7 +29 dx (7 +292 Example: 6. Logs and Exponentials Example: 7. The Chain Rule Example: If f(x) = ln(x), then df = 1x dx Iff(x)=ex,then df = dx If f(x) = eg(x), then df = dgeg(x) dx dx f(x) = ex2 df = 2xex2 dx Ifz=f(y)and y=g(x),then dz = dfdy dx dy dx z=y2,y=(x2+3x) dz = 2 2 + 3 ( 2 +329 dx...
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This note was uploaded on 04/05/2012 for the course ECN 437 taught by Professor Peterwilcoxen during the Spring '12 term at Syracuse.

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