f(x) = 2/x.
Find a formula for f^(n) (x), the n^th derivative of f(x), for any integer n is bigger or equal to 1.
Differentiation Question
2010-10-13 5:31 pm
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2010-10-14 12:42 am
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2010-10-13 6:02 pm
f(x) =2/x. Find a formula for f^(n) (x)，the n^thderivative of f(x)，for any integer n is bigger or equalto 1Solf(x)=2x^(－1)Set then^th derivative of f(x) is g(n，x)g(1，x)=－2x^(－2)g(2，x)=2*(1*2)x^(－3)g(3，x)=(－2)*(1*2*3)x^(－4)g(4，x)=2*(1*2*3*4)x^(－5)Sog(n，x)=(－1)^n*2*n!*x^(－n－1)the n^th derivative of f(x) is (－1)^n*2*n!*x^(－n－1)
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