If the derivative of f x with respect to x is 1-2-sin 2 x - f x then period of f x isA- 4 -B- -C- 2 -D- 3 -

The correct option is B πf'(x) = 1/2 sin^2 x/f(x)⇒ 2f(x). f'(x) = 1 2 sin^2x ⇒d/dx [f(x)]^2 = cos2x ⇒ f(x)^2 = ∫ cos2x dx = sin2x/2+c ∴ f(x) = ±√(sin2x/2)+ ...

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Byju's Answer

Standard XII

Mathematics

Quotient Rule of Differentiation

If the deriva...

Question

If the derivative of f(x) with respect to x is $\frac{\frac{1}{2} - s i n^{2} x}{f (x)}$ then period of f(x) is

π

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2 π

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3 π

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4 π

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Solution

The correct option is A $π$
$f^{'} (x) = \frac{\frac{1}{2} - s i n^{2} x}{f (x)} \Rightarrow 2 f (x) . f^{'} (x) = 1 - 2 s i n^{2} x$
$\Rightarrow \frac{d}{d x} [f (x)]^{2} = c o s 2 x$
$\Rightarrow f (x)^{2} = \int c o s 2 x d x = \frac{s i n 2 x}{2} + c$
$∴ f (x) = \pm \sqrt{\frac{s i n 2 x}{2}} + c \Rightarrow p e r i o d = π$

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If the derivative of f(x) with respect to x is 12−sin2xf(x) then period of f(x) is

The correct option is A πf′(x)=12−sin2xf(x)⇒2f(x).f′(x)=1−2sin2x ⇒ddx[f(x)]2=cos2x ⇒f(x)2=∫cos2x dx=sin2x2+c ∴f(x)=±√sin2x2+c⇒period=π

If the derivative of f(x) with respect to x is $\frac{\frac{1}{2} - s i n^{2} x}{f (x)}$ then period of f(x) is