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implicit derivative of (dy)/(dx),x=sec(1/y)

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implicit derivative dydx , x=sec(1y )

Solution

dydx =−y²sec(1y )tan(1y )

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Solution steps

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∫ tan(x)sec²(x)dx

Apply u-substitution: ∫ udu

=∫ udu

Apply the Power Rule: u²2

=u²2

Substitute back u=tan(x)

=tan²(x)2

Add a constant to the solution

=tan²(x)2 +C

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

implicit derivative of (dy)/(dx),x=sec(1/y)

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