If y-log 4sin xtan x then d y-d x at x-4 isA- -4-In 2B- -2-In 2C- -In 2D- -1-2 In 2

The correct option is A 4/In 2y =In tan x/In sin x ⇒ dy/dx =sec^2x/tan x.In sin x cos x/sin x. In tan x/{In(sin x)}^2 ⇒ dy/dx|_x=π/4 =2 In ( 1/√(2) )/{ In ( ...

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Byju's Answer

Standard XII

Mathematics

Property 1

If y=log 4sin...

Question

If $y = l o g_{s i n x} (t a n x) t h e n \frac{d y}{d x} a t x = \frac{π}{4}$ is

- \frac{4}{I n 2}

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- \frac{2}{I n 2}

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\frac{}{I n 2}

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- \frac{1}{2 I n 2}

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Solution

The correct option is A $- \frac{4}{I n 2}$
$y = \frac{I n t a n x}{I n s i n x} \Rightarrow \frac{d y}{d x} = \frac{\frac{s e c^{2} x}{t a n x} . I n s i n x - \frac{c o s x}{s i n x} . I n t a n x}{{I n (s i n x)}^{2}} \Rightarrow \frac{d y}{d x} |_{x = \frac{π}{4}} = \frac{2 I n (\frac{1}{\sqrt{2}})}{{I n (\frac{1}{\sqrt{2}})}^{2}} = \frac{2}{I n \frac{1}{\sqrt{2}}} = - \frac{2}{\frac{1}{2} I n 2} = - \frac{4}{I n 2}$

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If y=logsin x(tan x) then dydx at x=π4 is

The correct option is A −4In 2y=In tan xIn sin x⇒ dydx=sec2xtan x.In sin x−cos xsin x. In tan x{In(sin x)}2⇒ dydx|x=π4=2 In(1√2){In(1√2)}2=2In 1√2=−212 In 2=−4In 2

If $y = l o g_{s i n x} (t a n x) t h e n \frac{d y}{d x} a t x = \frac{π}{4}$ is