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Grade: Upto college level 

                        
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.
11 years ago

Answers : (1)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points 
							
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
6 years ago
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