Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2009-03-03 02:46:32

ganesh
Moderator

Offline

### Differential Calculus

1. Differentiate the following with respect to x.

(i)

(ii)

(iii)

2. Differentiate the following with respect to x.

(i)

(ii)

(iii)

3. Differentiate the following with respect to x.

(i)

(ii)

(iii)

(iv)

(v)

(vi)
.

Character is who you are when no one is looking.

## #2 2009-03-10 19:02:26

lady einstein
Novice

Offline

### Re: Differential Calculus

#2 i)
3 (3x^2 + 4x - 5)^2  *(6x + 4)

i beg to be pardoned for how i express my equations

## #3 2009-03-11 01:17:06

ganesh
Moderator

Offline

### Re: Differential Calculus

lady einstein,
Your answer is perfectly right!
The answer can be expressed in LaTeX by using the following code:-

#### Code:

$3\left(3x^{2}+4x-5\right)^{2} \cdot \left(6x+4\right)$

This would produce:

Character is who you are when no one is looking.

## #4 2009-06-25 18:36:18

glenn101
Full Member

Offline

### Re: Differential Calculus

1.(i) e^x
-----
cos(x)

Using Quotient Rule:
Let u=e^x, v=cos(x)
du/dx=e^x, dv/dx=-sin(x)

dy/dx=   v(du/dx)-u(dv/dx)
--------------------
cos^2(x)
=    cosx(e^x)-e^x(-sin(x))
----------------------------
cos^2(x)

=       -e^x(-cos(x)+sin(x))
-------------------------
cos^2(x)

(ii)    log(x)
------------
sin(x)
Using Quotient Rule:
Let u=log(x), v=sin(x)
du/dx= 1/x,  dv/dx=cos(x)

dy/dx=       v(du/dx)-u(dv/dx)
---------------------
v^2
=        sinx(1/x)-logx(cos(x))
-------------------------
sin^2(x)

=        sin(x)/x-logx(cos(x))
---------------------------
sin^2(x)
2. (i) y=(3x^2+4x-5)^3
Using Chain Rule:
Let u = 3x^2+4x-5, y=u^3
du/dx=6x+4       dy/du= 3u^2

dy/dx= 3(3x^2+4x-5)^2*(6x+4)

(ii) y=e^3x^2+2x+3
dy/dx=6x+2e^3x^2+2x+3
3. (i) y=e^2xcos(3x)
Using Product Rule:
Let u = e^2x,  v=cos(3x)
du/dx=2e^2x, dv/dx=-3sin(3x)

dy/dx= -e^2x(3sin(3x)+2e^2x(cos(3x))

I love Calculus:D
Also, just a suggestion Ganesh.
Could you perhaps make exercises for Integration?

Last edited by glenn101 (2009-06-25 18:39:45)

"If your going through hell, keep going."

## #5 2009-06-26 07:05:53

bobbym
Administrator

Offline

### Re: Differential Calculus

In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

## #6 2009-11-24 18:08:33

Denominator
Full Member

Offline

### Re: Differential Calculus

I think 2 ii is
(6x+2)e^(3x^2+2x+3)

## Board footer

Powered by FluxBB