# Multiply and differentiate (3x+12)(1-7x)?

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We'll use the the property of multiplication to be distibutive over addition:

(3x+12)(1-7x) = 3x + 3x*(-7x) + 12*1 + 12*(-7x)

(3x+12)(1-7x) = 3x - 21`x^(2)` + 12 - 84x

We'll combine like terms:

(3x+12)(1-7x) = -21`x^(2)` - 81x + 12

Now, we'll differentiate with respect to x:

d(3x+12)(1-7x)/dx = -42x - 81

**The requested result is d(3x+12)(1-7x)/dx = -42x - 81.**

`(3x+12)(1-7x)`

First, use First Outer Inner Last ( FOIL ) to multiply out this problem. Then, take the derivative by using the exponent rule and chain rule.

`(3x - 21x^2 + 12 - 74x)`

`(-21x^2 - 71x + 12)`

`dy/dx (-21x^2 - 71x + 12) =`

`-42x - 71`

``

`(3x+12)(1-7x) `

`3x xx 1 = 3x `

`3x xx -7x= -21x^2 `

`12xx1=12 `

`12xx-7x=-81x `

`-21x^2- 81x+3x + 12`

`-21x^2- 78x+ 12`

differentiation

**-42x - 78**