find the derivative of f(X)=x(3x-7)^3

Question

i think its the chain rule and product rule together

Answer 1

y = x( 3x - 7 )^3

dy/dx = d(x)*(3x - 7 )^3 + x * d((3x - 7 )^3)

dy/dx = ( 3x - 7 )^3 + x( 3(3x - 7 )^2*d(3x - 7))

dy/dx = ( 3x - 7 )^3 + x(3( 3x - 7 )^2 * 3)

dy/dx = ( 3x - 7 )^3 + 9x(3x - 7 )^2

dy/dx = ( ( 3x - 7 ) ^2)* [( 3x - 7 ) + 9x]

dy/dx = ((3x - 7 )^2) * (12x -7)