Question

dx/dy; if y= (2x+9)/(5x-4)

Answer 1

Given :-

• y = (2x + 9)(5x - 4) .

To Find :-

• The derivative of the given function .

Answer :-

Here , the given function given to us is ,

⇒ y = (2x + 9)/( 5x - 4 ) .

The given function is in the form of u/v , that is if ,

⇒ y = u/v , then

⇒ dy/dx = ( v. du/dx - u . dv/dx ) / v²

Here ,

• u = 2x + 9
• v = 5x - 4

So , that ,

⇒ dy/dx = (5x -4) d(2x+9)/dx - (2x+9) d(5x - 4)/v²

⇒ dy/dx = (5x - 4) × 2 - (2x + 9) × 5 / (5x-4)²

⇒ dy/dx = 10x - 8 -10x - 45 / (5x - 4)²

⇒ dy/dx = -53/ ( 5x - 4 )²

Hence the required derivative of the function is -53/(5x - 4)² .