if 2​x +2​y =2x+y , then dy/dx is equal to
 

Dear student
2x+2y=2x+yDifferentiating both sides, we getddx2x+2y=ddx2x+yddx2x+ddx2y=log2. 2x+y.ddxx+ylog2. 2x+log2. 2y. dydx=log2dxdx+dydx.2x+ylog2. 2x+log2 .y'. 2y=log2 1+y'. 2x+ylog2 .2x+log2 .2y y'=log2 .2x+y 1+y'log2 .2x+log2 .2y y'=log2.2x+y +log2 .2x+y. y'y'log2 .2y-log2 .2x+y=log2.2x+y -log2 .2xy'=log2.2x+y -log2 .2xlog2 .2y-log2 .2x+yy'=2x+y -2x2y-2x+yy'=-2x+y -2x2x+y-2y
Regards

  • -1
Take log and differenciate each term with respect to x. Then the ans
dy/dx= (1-2^x)/ 2^y-1)
  • 2
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