Differentiate 3x^4 + 2x^3 - x / x.
My answer is 9x^2 + 4x but actual answer given is 9x^2 + 4x -1( which I think is wrong)
Please check, thanks.
Next, differentiate 5x^0.5 / x-3
I got -5 (x^0.5 - x + 3) / 2x^0.5 (x -3)^2
It wants me to express in the form of -a (x +b) / 2x^0.5 (x-3)^2
However, do you notice that there's the term x^0.5 for denominator? How am I supposed to merge that with term x?
You mean
y = (3x^4 + 2x^3 -x)/x
y = 3x^3 + 2x^2 -1
dy/dx = (3)(3)(x^2) + 2(2)x - 0
dy/dx = 9x^2 + 4x Then you are right.
y = (5x^0.5)/(x-3)
dy/dx = [(2.5x^-0.5)(x-3) - (1)(5x^0.5)]/(x-3)^2
take out common of x^-0.5 on the numerator & multiply by 2/2
dy/dx = {x^-0.5[ 5(x-3)- 10(x)]}/2(x-3)^2
Take x^-0.5 to the denominator
dy/dx = (-5x-15)/2x^0.5(x-2)^2
dy/dx = -3(x+5)//2x^0.5(x-2)^2