Find the derivative of y 1 9x210Solution Use the chain rul

Find the derivative of y = (1 - 9x2)10

Solution

Use the chain rule, d/dx((1-9 x^2)^10) = ( du^10)/( du) ( du)/( dx), where u = 1-9 x^2 and ( du^10)/( du) = 10 u^9: = 10 (1-9 x^2)^9 (d/dx(1-9 x^2)) Differentiate the sum term by term and factor out constants: = 10 (1-9 x^2)^9 (d/dx(1)-9 (d/dx(x^2))) The derivative of 1 is zero: = 10 (1-9 x^2)^9 (0-9 (d/dx(x^2))) The derivative of x^2 is 2 x: = -90 (1-9 x^2)^9 (2 x)