Question

Find derivative of f(x). F(x) = (x^3+x^2-x)/(sqrt(x) +3).

Answer 1

use quotient rule

Answer 2

treat this as u/v form and differentiate.

Answer 3

Remember that √x = x^½ and 1/√x = x^-½

Also remember that d(x^k)/dx = kx^(k-1)

So d(u^½) = ½u^-½ * du/dx (using the chain rule).

In this case, u = 5 - 3x and du/dx = -3

d[√(5 - 3x)] = ½/√(5 - 3x) * -3 = -3/[2√(5 - 3x)]

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Let u = 2 - 9x so du/dx = -9

d[-3(2 - 9x)^(1/3) = d[-3u^(1/3)]/dx
d[-3(2 - 9x)^(1/3) = -3d[u^(1/3)]/dx
d[-3(2 - 9x)^(1/3) = -3*(1/3)u^(-2/3) * du/dx
d[-3(2 - 9x)^(1/3) = -(2 - 9x)^(-2/3) * -9

d[-3(2 - 9x)^(1/3) = 9/(2 - 9x)^(2/3)

Answer 4

lol! copy pasted from here...
http://answers.yahoo.com/question/index?qid=20081018075010AA7klAr
an that too wrong sum... :P

Answer 5

Here u=(x^3+x^2-x) and v=(sqrt(x) +3)

Can u do nw?