What is the f'(x) of this equation?

Question

(2x+7)^-1....Do I apply the chain rule?

Answer 1

yes, -(2x+7)^-2 * 2 = -2/(2x+7)^2

Answer 2

These other people are mistaken my friend, the chain rule is not required to differentiate this problem. Remember that anything raised to the -1 power is equivalent to the same expression over 1. So f(x)=1/(2x+7), Now apply the formula for differentiation of one value divided by the other:

d/dx[u/v]=(vu'-uv')/v^2

so: ((2x+7)*0 - 1*2)/(2x+7)^2
= -2/(2x+7)^2

Always look to see if there is any way to simplify or rearrange an equation before you jump in and get stuck doing more work than is necessary. This will be very important in your Calculus courses. Hope this helped.

Answer 3

Yes, apply the chain rule.

(-1(2x + 7)^-2)*2

-2(2x + 7)^-2

Answer 4

what else would you apply other than the chain rule? if you applied anything else, it would be wrong.

Answer 5

f ( x) = (2x + 7) ^(-1)
f ' (x) = ( -1 ) (2x + 7) ^(-2) (2)
f ' (x) = ( -2 ) / (2x + 7) ²

OR

let u = 2x + 7
du / dx = 2
y = u ^(-1)
dy / du = (-1) u ^(-2)
dy / du = (-1) / u ²
dy/dx = (dy/du) (du/dx)
dy/dx = (-1) / u² (2)
dy/dx = (-2) / (2x + 7) ²