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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
- lady einstein
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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
lady einstein,
Your answer is perfectly right!
The answer can be expressed in LaTeX by using the following code:-
Code:
[math]3\left(3x^{2}+4x-5\right)^{2} \cdot \left(6x+4\right)[/math]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
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Re: Differential Calculus
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.