How to find the derivative of y=sin(x+y)?

Carsen Oneill

Carsen Oneill

Answered question

2023-02-01

How to find the derivative of y = sin ( x + y ) ?

Answer & Explanation

Holden Flowers

Holden Flowers

Beginner2023-02-02Added 4 answers

You simply differentiate both sides with respect to x . The left side would simply give you d y d x . However, you must use the chain rule for derivatives of composite functions for the right side (functions of functions). Thus
d d x ( sin ( x + y ) ) = cos ( x + y ) × d d x ( x + y ) = cos ( x + y ) ( 1 + d y d x )
Thus, we get
d y d x = cos ( x + y ) ( 1 + d y d x )
We can easily solve this for the quantity d y d x :
( 1 - ( cos ( x + y ) ) d y d x = cos ( x + y ) d y d x = cos ( x + y ) 1 - cos ( x + y )

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