Prove the general power rule of derivatives using the inverse

Kelly Nelson 2021-12-11 Answered

Prove the general power rule of derivatives using the inverse property (xn=enlnx)?

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Expert Answer

Fasaniu
Answered 2021-12-12 Author has 46 answers
Step 1
The general power rule:
ddx(xn)=nxn1
Step 2
Proof:
ddx(xn)=ddx(enlnx)   [xn=enlnx]
=enlnxddx(nlnx)
=enlnxnx
=xn×nx   [xn=enlnx]
=nxn1
Thus, the general power rule proved.
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