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Find the derivative of sinx to the poer n like square 2 cube 3 its poer is 3, by first principle method.

Find the derivative of sinx to the poer n like square 2 cube 3 its poer is 3, by first principle method.

Grade:Upto college level

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
f`(x) = \lim_{h\rightarrow 0} \frac{f(x+h) - f(x)}{h}
f(x) = sin ^{2} x
f`(x) = \lim_{h\rightarrow 0} \frac{sin ^{2} (x+h) - sin ^{2} x}{h}
f`(x) = \lim_{h\rightarrow 0} \frac{(sin (x+h) + sin x).(sin(x+h) - sin x)}{h}
f`(x) = \lim_{h\rightarrow 0} \frac{4 sin(x+h/2).cos(h/2). cos(x+h/2).sin(h/2)}{h}
f`(x) = \lim_{h\rightarrow 0} \frac{sin(h/2)}{h/2}.2 sin(x).cos(0). cos (x)
f`(x) = 1.2 sin(x). cos (x)
f'(x) = sin (2x)
Thanks & Regards
Bharat Bajaj
askiitian faculty
IIT Delhi

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