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## #1 2009-03-03 02:46:32

ganesh
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### 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

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### 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
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### Re: Differential Calculus

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

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### 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

Online

### Re: Differential Calculus

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #6 2009-11-24 18:08:33

Denominator
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### Re: Differential Calculus

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