2. 2x 3y sin y

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Solution

The given equation is,

2x+3y=siny

Differentiate on both sides of the above equation.

d( 2x+3y )=d( siny ) d( 2x )+d( 3y )=cosydy 2dx+3dy=cosydy cosydy−3dy=2dx

Further solve the equation.

( cosy−3 )dy=2dx dy dx = 2 cosy−3

Thus, the derivative of 2x+3y=siny is dy dx = 2 cosy−3 .

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