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Differentiate the following function wit...

Differentiate the following function with respect to `x` from first principle: `x^(-3//2)`

Text Solution

Verified by Experts

`f(x)=x^3-27`
`f'(x)=lim_(h->0) frac{f(x+h)-f(x)}{h}`
`=lim_(h->0) frac{(x+h)^3-27-(x^3-27)}{h}`
`=lim_(h->0)frac{h^3+3x^2h+3xh^2}{h}`
`=3x^2`
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