Thread: Substitution
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Old April 30th, 2008, 01:36 PM
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Hi
L(x^m)= \frac{\mathrm{d^2}}{\mathrm{d}x^2}(x^m) -2 \frac{1}{x}\frac{\mathrm{d}}{\mathrm{d}x}(x^m) +2\frac{x^m}{x^2}
Using the derivatives you've evaluated :
L(x^m)= m(m-1)x^{m-2}-2\frac{mx^{m-1}}{x}+2\frac{x^m}{x^2}=m(m-1)x^{m-2}-2mx^{m-2}+2x^{m-2}

Factor by x^{m-2} and you get L(x^m)=(m(m-1)-2m+2)x^{m-2}
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