Differantiate?

Question

(x-2)(2x+3)

x2+1/x

(x+1/x)2

Answer 1

Hi,

First expand problems if possible. Then differentiate.

(x-2)(2x+3) = 2x² - x - 6

d/dx(2x² - x - 6) = 4x - 1 <== answer

You can also do this as d/dx(uv) = uv' + u'v

(x - 2)d/dx(2x+3) + d/dx(x - 2)*(2x+3) =
(x - 2)(2) + 1(2x + 3) = 2x - 4 + 2x + 3 = 4x - 1 <== answer



x²+1/x = x² + x^(-1)

d/dx(x² + x^(-1)) = 2x - x^(-2) = 2x - 1/x² <== answer





(x+1/x)² = x² + 2 + 1/x² = x² + 2 + x^(-2)

d/dx(x² + 2 + x^(-2)) = 2x - 2x^(-3) = 2x - 2/x³ <== answer


I hope those help!! :-)

Answer 2

a)use product rule
uv'+vu'
let u = x-2
u' = 1
v=2x+3
v'=2
(x-2)(2)+(2x+3)(1)
= 2x-4+2x+3
=4x-1

b) x2+1/x
=2x-1/x^2

c)defferentiate the bracket after that differentate inside the bracket
2(x+1/x)(1+1/x^2)

Answer 3

These are term-by-term differentiations.
In the first, you have to determine the 3-term quadratic.
In the second, you differentiate each term
In the last, you also determine the three-term expression and then differentiate.

The power rule for differentiation is
A * x ^ n = n* A * x^(n-1)
this holds for all real n, positive or negative.

Answer 4

For the first equation, you can simply differentiate each set of parentheses individually and then multiply them together without having to simplify the equation.

The second equation- just differentiate each part and add them together.

The third must be simplified first by multiplying each of the inside terms by 2, then differentiating them individually and then adding them together.

Note: learn to spell check before you go public with the computer. You lose a lot of credibility when the world sees you as ignorant. This is a common problem amongst youth today- including my children, darn it! That is why God gave us spelling checkers...

Answer 5

First, distribute the equation.
2xsquared -x-6
then differentiate.
2x-1