1.

If y=tan(x+y), then find dy/dx

Answer»

ANSWER:

sec² ( X + y ) / ( 1 - sec² ( x + y )

Step-by-step explanation:

GIVEN :

y = tan ( x + y )

Diff. w.r.t. x :

d y / d x = sec² ( x + y ) . ( x + y )'

= > y' = sec² ( x + y ) . ( ( x )' + ( y )' )

= > y' = sec² ( x + y ) . ( 1 + y' )

= > y' = sec² ( x + y ) + y' ( sec² ( x + y ) )

= > y' - y' ( sec² ( x + y ) ) = sec² ( x + y )

= > y' ( 1 - sec² ( x + y ) ) = sec² ( x + y )

= > y' = sec² ( x + y ) / ( 1 - sec² ( x + y )

Therefore , d y / d x of given function y = tan ( x + y ) is sec² ( x + y ) / ( 1 - sec² ( x + y )


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