confuse about the rules of derivative

Discussion in 'Math' started by faraz101, Apr 12, 2009.

  1. faraz101

    Thread Starter New Member

    Apr 12, 2009
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    0
    guys i am too much confused about the derivative rules.i am very weak in calculus.I have no idea that which rule to apply for which equation for example i have this equation
    find the indicated derivative

    dy/dx if y=x^3+7/x
    here i applied quotient rule but my friend tolled me that we can't apply quotient rule here.i dont know why?
    are there such rules exists which are helpful in determining hat what rule should i apply?
    thanx
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    You can apply the quotient rule to the 7/x term. It's a simple quotient. You can't always believe everything your friends say.

    Once you "get it" you'll be doing problems like this in your head! It just takes time and lot's of practice.
     
  3. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Of course you can use the division rule.

    You can also convert 7/x to 7*x^-1 and differentiate it.
     
  4. faraz101

    Thread Starter New Member

    Apr 12, 2009
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    thanx for ur reply friends.but how can i decide in this case that what rule should i apoly in following example
    here
    y= sin^3x
    here i applied simple power rule and after diff i got
    y=3sin^2x
    but in solution manual writer has applied chain rule
     
  5. vvkannan

    Active Member

    Aug 9, 2008
    138
    11
    Hello faraz
    In general we apply chain rule when a function is composite .
    Here you get 3 sin ²x (cos x) .The cosx coming from the differentiation of the sinx.
    Read this tutorial
    http://web.mit.edu/wwmath/calculus/differentiation/chain.html
    It has nice examples.Hopefully you will understand more
     
  6. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    You can use the quotient rule on 7/x, but it's not very smart to do this. As mik3 points out, you can rewrite 7/x as 7*x^(-1) and use the constant multiplier rule (d/dx(k*f(x)) = k*d/dx(f(x)) and the power rule (d/dx(x^n) = nx^(n - 1)). For another example, if y = x/3 and you wanted to find dy/dx, you could use the quotient rule, but it would again be a lot of wasted effort, and would be simple to use the constant multiplier rule.

    Save the quotient rule for expressions like f(x) / g(x), where neither f(x) nor g(x) are constant functions.
     
  7. mik3

    Senior Member

    Feb 4, 2008
    4,846
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    Apply the chain rule always as to be correct. It works for simple functions too.
     
  8. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    I disagree, but maybe I'm not understanding what you said. You should use the chain rule only when you're working with a composite function, such as cos(2x).

    In general, you should always use the simplest rule that applies. For example, to differentiate y = 3x, you could use the product rule, but it would be better to use the constant multiple rule.

    To differentiate y = x/2, you could use the quotient rule, but again, the constant multiple rule is the one to use here, since x/2 = 1/2 * x.
     
  9. josephcarney121

    New Member

    Oct 12, 2007
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    you can also use the exponent rule which is the simplest.

    dy/dx if y=x^3+7/x is also = x^3 + 7x^-1 therefore dy/dx=3x^2 -7x^-2 or in its original form 3x^3-7/x^2.
     
  10. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    This rule is usually called the power rule, and has already been mentioned.
     
  11. swarn kamal

    New Member

    May 5, 2009
    3
    0
    dy/dx if y=x^3+7/x

    hi... it's a very simple problem... here we would not use any complicated rules to diffrentiate it... you just appply simple derivative formula to diffrentiate it with respect to 'x'...
    It's solution is:
    1). we will diffrentiate "x^3" simply by applying the formula d(x^n)/dx = nx^(n-1).
    2.) then we will diffrentiate 7/x as: 7 is a constant so we will diffrentiate only 1/x by applying the formula of d/dx(1/x)....
    3.) and the answer is dy/dx = 3x^2 - 7/x^2.
     
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