How do you use the limit definition of the derivative to find the derivative of f(x)=1/x?

1 answer:

6 0

Example 1. Let us start with the functionf(x) = x2. We have

So

which means f '(a) = 2a.

What about the derivative of f(x) = xn. Similar calculations, using the binomial expansion for (x+y)n (Pascal's Triangle), yield

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il63 [147K]

The required value after simplification of the s = -16/3. None of these are correct.

Given that,
To simplify $[\frac{x^{2/3}x^{-1/2}}{x\sqrt{x^3}\sqrt[3]{x}}]^2$ and to find the value of s in $x^s$ .

<h3>What is simplification?</h3>

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Simplification,

$=[\frac{x^{2/3}x^{-1/2}}{x\sqrt{x^3}\sqrt[3]{x}}]^2\\= \frac{x^{4/3}x^{-1}}{x^2x^3*{x}^{2/3}}\\= \frac{x^{1/3}}{x^{17/3}}\\=x^{-16/3}$
Comparing with $x^S$
s = -16/3