f(x)=sin²x,find f'(x) for it.
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we have given f(x) = sin²x
and we want to find f'(x) , means we want to find first derivative of f(x).
we know, first derivative of sine is cosine.
e.g., d(sinx)/dx = cosx
so, f(x) = sin²x
differentiate both sides with respect to x,
d(f(x))/dx = d(sin²x)/dx
f'(x) = 2sinx × d(sinx)/dx
= 2sinx × cosx
= sin2x [ because we know, sin2A = 2sinA.cosA]
hence, f'(x) = sin2x
and we want to find f'(x) , means we want to find first derivative of f(x).
we know, first derivative of sine is cosine.
e.g., d(sinx)/dx = cosx
so, f(x) = sin²x
differentiate both sides with respect to x,
d(f(x))/dx = d(sin²x)/dx
f'(x) = 2sinx × d(sinx)/dx
= 2sinx × cosx
= sin2x [ because we know, sin2A = 2sinA.cosA]
hence, f'(x) = sin2x
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