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Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=(x+1)(3x-4)x3-27

Short Answer

Expert verified

The required answer is-7x3-27-x+13x-43x22x3-27x3-272

Step by step solution

01

Step 1. Given Information   

The given function isf(x)=(x+1)(3x-4)x3-27

02

Step 2. Calculation   

Differentiate both the sides with respect to x, we get,

f'(x)=ddxx+1(3x-4x3-27-x+13x-4ddxx3-27x3-272=ddxx+1(3x-4)-x+1ddx3x-4x3-27-x+1(3x-4)12x3-27-12ddxx3-27x3-272=(3x-4)-3x+1x3-27-x+1(3x-4)3x22x3-27x3-272=3x-4-3x-3x3-27-x+1(3x-4)3x22x3-27x3-272=-7x3-27-x+1(3x-4)3x22x3-27x3-272

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