maths help needed......... urgently......?

Question

(x+1)^3 (2x-5)^2

can some1 plz...plz..go through it in detail....and can u tell me what happens 2 the powers wen its all been differentiated...i mean after..... wen its all bein multiplied and added 2gether...

thanx...

4got 2 add that it's got 2 b differentiated using the product rule.....

u(dv/dx) + v(du/dx)

Answer 1

To differentiate this:

Let u = (x+1)^3, and v = (2x-5)^2.

Then, by the product rule, the derivative is

(2x-5)^2 * d/dx[(x+1)^3] + (x+1)^3 d/dx[(2x-5)^2].

Now, to differentiate (x+1)^3, use the chain rule, combined with the power rule,

d/dx[f(x)^n] = nf(x)^(n-1)f'(x)

to obtain

d/dx[(x+1)^3] = 3(x+1)^2*d/dx[(x+1)]
= 3(x+1)^2.

Similar for (2x-5)^2.

I'm not sure exactly what you mean by the last part of the question, about "what happens to the powers".

Answer 2

Im doing the first one and then you can do the second one because if you can follow the directions to the first, you can do the second one.

(X+1)^3 breaks up to (X+1)(x+1)(X+1). Now take only X+1 times X+1 for now.

Multiply by components. X+1 times X = x^2 + X. Then multiple X + 1 by 1 = X +1.

Add the results together: X^2 + X + x + 1 = X^2 + 2x + 1. Multiply this by the final X + 1 in the same way.

X^2 + 2x + 1 times X = X ^ 3 + 2x^2 + x , X^2 + 2x + 1 times +1 = X^2 + 2x + 1 .

Add them together to get X^3 + 3x^2 + 3x + 1

Answer 3

General formulas
(a + b)^3 = a^3 + 3 a^2 b + 3 a b^2 + b^3
(a - b)^2 = a^2 - 2 a b + b^2

So here
(x + 1)^3 = x^3 + 3 x^2 + 3 x + 1
(2x - 5)^2 = 4x^2 - 20x + 25

Now we have to multiply these:
(x^3 + 3 x^2 + 3 x + 1) (4x^2 - 20x + 25)

That gives
4x^5 + 12x^4 + 12x^3 + 4x^2
-20x^4 - 60x^3 - 60x^2 - 20x
25x^3 + 75x^2 + 75x + 25

which must be added together; just add like terms:
4x^5 - 8x^4 - 23x^3 + 19x^2 + 55x + 25

Answer 4

First of all it might be easier to use a substitution. Since the power rule uses u(dv/dx) + v(du/dx) we should use u and v as our substitutes.

Let u = x + 1 then du/dx = 1
Let v = 2x -5 then dv/dx = 2

Now we can rewrite our equation as:
f(x) = u^3v^2
and differentiate:
df/duv = 3u^2(du/dx)v^2 + 2v(dv/dx)u^3
= 3u^2(1)v^2 + 2v(2)u^3
= 3u^2v^2 + 4vu^3

Now we can replace our u and v with our orginal f(x) as:
f'(x) = 3(x+1)^2(2x-5)^2 + 4(2x-5)(x+1)^3

The above equation is your first derivative. Hopefully you can simple expand it and add all of the like terms yourself. If you cannot, I recommend returning to algebra and beefing up on your fundamentals. One other suggestion I have is to NOT write as if you were sending a text message. It makes it difficult to understand what you are saying. You have a keyboard - use it.

Answer 5

u'll have to do a doulble diffentiation here.
(x+1)^3 (2x-5)^2
product rule, u(dv/dx) + v(du/dx)

u = (x+1)^3 v = (2x-5)^2
du/dx = 3(x+1)^2 dv/dx = 2x-5
total diff = (x+1)^3(2x-5) +(2x-5)^2[3(x+1)^2]

work out the rest i aint able to do the entire thing....dont be lazy

Answer 6

(x+1)^3 = (x+1)*(x+1)*(x+1)
= (x^2+2x+1)*(x+1)
= x^3+3x^2+3x+1

(2x-5)^2 = (2x-5)*(2x-5)
= 4x^2-20x+25

my bad... you are supposed to multiply...
(x^3+3x^2+3x+1)(4x^2-20x+25)
= 4x^5-20x^4+25x^3+12x^4-60x^3+75x^2+12x^3-60x^2+75x+4x^2-20x+25

= 4x^5-18x^4-23x^3+19x^2+55x+25