Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

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)

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

lady einstein

Member

Registered: 2009-02-17

Posts: 7

Re: Differential Calculus

#2 i)
3 (3x^2 + 4x - 5)^2  *(6x + 4)

i beg to be pardoned for how i express my equations

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Differential Calculus

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

This would produce:

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

glenn101

Member

Registered: 2008-04-02

Posts: 108

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 (2009-06-24 20:39:45)

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"If your going through hell, keep going."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Differential Calculus

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Denominator

Member

Registered: 2009-11-23

Posts: 220

Re: Differential Calculus

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

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