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How d n /dx n becomes d n-1 /dx n-1 …...please explain

How dn/dxn  becomes dn-1/dxn-1 …...please explain 

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Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Hello student,
Please find answer to your question
y = f(x)
\frac{d^{n}}{dx^{n}}(f(x)) = \frac{d^{n-1}}{dx^{n-1}}(f'(x)) = \frac{d^{n-2}}{dx^{n-2}}(f''(x)) = ...........
For example,
f(x) = (x+1)^{4}
\frac{d^{4}}{dx^{4}}(x+1)^{4} = 4!
Apply this
\frac{d^{n}}{dx^{n}}(f(x)) = \frac{d^{n-1}}{dx^{n-1}}(f'(x)) = \frac{d^{n-2}}{dx^{n-2}}(f''(x)) = ...........
\frac{d^{4}}{dx^{4}}(x+1)^{4} = \frac{d^{3}}{dx^{3}}(4(x+1)^{3}) = \frac{d^{2}}{dx^{2}}(4.3(x+1)^{2}) = \frac{d}{dx}(4.3.2.(x+1)) = 4!

f(x) = x^{n}log(x)
\frac{d^{n}}{dx^{n}}(f(x)) = \frac{d^{n-1}}{dx^{n-1}}(f'(x))
I_{n} = \frac{d^{n-1}}{dx^{n-1}}(x^{n}log(x))'
I_{n} = \frac{d^{n-1}}{dx^{n-1}}(x^{n}.\frac{1}{x}+log(x).nx^{n-1})
I_{n} = \frac{d^{n-1}}{dx^{n-1}}(x^{n-1}+nx^{n-1}log(x))
milind
23 Points
9 years ago
Thanx …........you are awesome sir …....you helped me whenever I required …..this website is awesome ….....

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