# confuse about the rules of derivative

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

1. ### faraz101 Thread Starter New Member

Apr 12, 2009
2
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
790
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
69
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
2
0
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.
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
69
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
1
0
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.