if y cos 1 sin 4 x find dy dx Find dy dx if y e 5x 2 2x 4 If x t is a differentiable function of t then prove that int f x dx int f t t dt Hence find int logx n x dx If y log x sqrt x 2 a 2 sqrt x 2 a 2 x find dy dx If y tan 1 6x 7 6
Replace y y with dy dx d y d x dy dx cos cos x sin x d y d x cos cos x sin x Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor Explanation y sin4x cos4x Use the chain rule to differentiate The chain rule states that f g x f g x g x dy dx 4sin3x cosx 4cos3x sinx dy dx 4sin3xcosx 4sinxcos3x Use the following trigonometric identities to simplify sin2x cos2x 1 sin 2x 2sinxcosx
if y cos 1 sin 4 x find dy dx
if y cos 1 sin 4 x find dy dx
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Solved Consider The Following Differential Equation sin y Chegg
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Ex 9 4 1 Find General Solution Dy dx 1 Cos X 1 cosx
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Replace y y with dy dx d y d x dy dx 1 1 sin x d y d x 1 1 sin x Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor Find dy dx for y sin 1 cosx where x 0 2 View Solution Click here point up 2 to get an answer to your question writing hand let ysin1cos x then find dfracdydx
Show that dy dx y x 1 3 If x a 2 sin 2 and y a 1 cos 2 find dy dx when theta pi 3 If X f t and Y g t Are Differentiable Functions of t then prove that y is a differentiable function of x and dy dx dy dt dx dt where dx dt 0 Hence find dy dx if x a cos 2 t Solution Verified by Toppr Given cosx y siny x taking log on both sides we get ylogcosx xlogsiny y 1 cosx sinx logcosxdy dx x 1 siny cosy dy dx logsiny 1 ytanx logcosxdy dx xcotydy dx logsiny 1 logcosxdy dx xcotydy dx logsiny ytanx dy dx logcosx xcoty logsiny ytanx upon further simplification we get
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Because when x lies in range pi 4 3pi 4 then sin x cos x therefore sin x cos x is positive and while we taking log on sin x cos x it must be positive If y sin x cos x sin x cos x pi 4 x 3pi 4 then find dy dx Example 23 Find if y sin y cos y sin y cos x Differentiating both sides by x sin sin sin x sin x cos y sin x 1 cos y sin x
Example 34 Find Dy dx If X A Cos Theta Y A Sin Examples
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if y cos 1 sin 4 x find dy dx - If cos y x cos a y with cos a neq pm 1 then prove that dfrac dy dx dfrac cos 2 a y sin a Hence show that sin a dfrac d 2 y dx 2 sin 2 a y dfrac dy dx 0