Find the derivative of y x3 3x 2 x2 1Solution Use the q

Find the derivative of y = x3 + 3x + 2 / x2 - 1

Solution

Use the quotient rule, d/dx(u/v) = (v ( du)/( dx)-u ( dv)/( dx))/v^2, where u = x^3+3 x+2 and v = x^2-1: = ((x^2-1) (d/dx(x^3+3 x+2))-(x^3+3 x+2) (d/dx(x^2-1)))/(x^2-1)^2 Differentiate the sum term by term: = ((x^2-1) (d/dx(x^3+3 x+2))-(x^3+3 x+2) (d/dx(x^2)+d/dx(-1)))/(x^2-1)^2 Differentiate the sum term by term and factor out constants: = ((x^2-1) (d/dx(x^3)+d/dx(2)+3 (d/dx(x)))-(x^3+3 x+2) (d/dx(x^2)+d/dx(-1)))/(x^2-1)^2 The derivative of -1 is zero: = ((x^2-1) (d/dx(x^3)+3 (d/dx(x))+d/dx(2))-(x^3+3 x+2) (d/dx(x^2)+0))/(x^2-1)^2 The derivative of 2 is zero: = ((x^2-1) (d/dx(x^3)+3 (d/dx(x))+0)-(x^3+3 x+2) (d/dx(x^2)))/(x^2-1)^2 The derivative of x^2 is 2 x: = ((x^2-1) (d/dx(x^3)+3 (d/dx(x)))-(x^3+3 x+2) (2 x))/(x^2-1)^2 The derivative of x is 1: = ((x^2-1) (d/dx(x^3)+3)-2 x (x^3+3 x+2))/(x^2-1)^2 The derivative of x^3 is 3 x^2: = ((x^2-1) (3 x^2+3)-2 x (x^3+3 x+2))/(x^2-1)^2