How do you find the derivative of #f(x)=(x+1)(x^2+2x-3)#?

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Answer 1 · 2017-07-02T19:28:54

#(df)/dx = 3x^2+6x-1#

We can multiply the two polynomials:

#f(x) = (x+1)(x^2+2x-3)#

#f(x) = x^3+2x^2-3x+x^2+2x-3#

#f(x) = x^3+3x^2-x-3#

Then differentiate:

#(df)/dx = 3x^2+6x-1#

Alternatively we can use the product rule:

#(df)/dx = d/dx (x+1) xx (x^2+2x-3)+ (x+1) xx d/dx(x^2+2x-3)#

#(df)/dx = (x^2+2x-3)+ (x+1) (2x+2)#

#(df)/dx = (x^2+2x-3)+ (2x^2+4x+2)#

#(df)/dx = 3x^2+6x-1#