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

 

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.

 

Of course you can use the division rule.

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

 

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

 

.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

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

 

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

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.

 

Apply the chain rule always as to be correct. It works for simple functions too.

 

Apply the chain rule always as to be correct. It works for simple functions too.

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.

 

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.

 

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.

This rule is usually called the power rule, and has already been mentioned.

 

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.