Question

Find a derivative of x square-2 at x=10

Answer 1

ans:2x is the derivative of x square -2 and its value is 20 at x=10

Answer 2

Answer:

$f(x) = x ^{2} - 2 \\ f(x + h) = (x + h)^{2} - 2 \\ Now, \\ \\ f'(x)= \frac{f(x + h) - f(x)}{h} \\ \displaystyle \lim_{h \to 0} = \frac{(x + h)^{2} - 2 - (x^{2} - 2)}{h} \\ \displaystyle \lim_{h \to 0} = \frac{x ^{2} + h^{2} + 2xh-2 - x^{2} + 2}{h} \\\displaystyle \lim_{h \to 0} = \frac{\cancel{x ^{2}} + h ^{2} + 2xh \: \cancel{ -2} \: \: \: \cancel{-x^{2}} \: \cancel { + 2}}{h} \\ \displaystyle \lim_{h \to 0} = \frac{h^{2} + 2xh }{h} \\\displaystyle \lim_{h \to 0} = h + 2x \\ = 0 + 2x \\ = 2x$

f'(x) = 2x

f'(10) = 2*10

‎‎‎‎‎‎ ‎ ‎ ‎‎ ‎ ‎ ‎‎ ‎ ‎=20

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