How do you find derivatives using the first principle in NCERT Class 11 Maths?
Answer (1)
To find derivatives using the first principle, we use the definition:
$
f^{\prime}(x)=\lim\limits_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}
$
Steps to Find the Derivative Using the First Principle:
1. Substitute $f(x+h)$ into the formula.
2. Find $f(x+h)-f(x)$.
3. Simplify the expression and divide by $h$.
4. Apply the limit $h \rightarrow 0$.
Example: $f(x)=x^2$
$
f^{\prime}(x)=\lim\limits_{h \rightarrow 0} \frac{(x+h)^2-x^2}{h}=\lim\limits_{h \rightarrow 0} \frac{x^2+2 x h+h^2-x^2}{h}=\lim\limits_{h \rightarrow 0}(2 x+h)=2 x
$
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