Differentiating with respect to 'x' help

[Brinkley23]

Hi All,

Im in the process of learning calculus and have been given a question to answer, which I have made an attempt at solving (below), can you please advise if I am correct or not, many thanks in advance.

differentiate with respect to 'x'

y=2x⁴ + 3x^-2 + 9

what I have work out:

using rule 1 - anx^n-1 and rule 5 - any constant is equal to 0

dy/dx = 8x³ - 6^-3 + 0

dy/dx = 8x³ - 6x^-3 ............................ [edited]

Sorry if I am way off, its my first attempt. Thanks

 

[JeffM]

It is correct

Actually you used more rules than just two. But you used them all correctly.

 

[Brinkley23]

It is correct

Actually you used more rules than just two. But you used them all correctly.

Thanks for the quick reply JeffM, glad to know that I got the correct answer!

Can you check over this one for me:

y=5e^3x - 8e^-2x

My workings out using rule 4: na e^ax

dy/dx = 15e^3x - 16e^-2x

Many Thanks

 

[JeffM]

(-8)(-2) = ?

 

[Brinkley23]

(-8)(-2) = ?

now this is where my basic math skills really let me down! knowing that a negative multiplied by a negative results in a positive I would expect the answer 16.

therefore dy/dx = 15e^3x + 16e^-2x ?

 

[Brinkley23]

now this is where my basic math skills really let me down! knowing that a negative multiplied by a negative results in a positive I would expect the answer 16.

therefore dy/dx = 15e^3x + 16e^-2x ?

oh and seeing as I've got you... (last one I promise)

y= 6sin3x - cos2x

My working out using rule 2: na cos ax and 3: -na sin ax

dy/dx = 18cos3x -sin2x ? (I'm sure with this one I'm a mile off, I was unsure if rule 3 was correct to apply for the 2nd part and if I have used it correctly?!)

 

[LCKurtz]

oh and seeing as I've got you... (last one I promise)

y= 6sin3x - cos2x

My working out using rule 2: na cos ax and 3: -na sin ax

dy/dx = 18cos3x -sin2x ? (I'm sure with this one I'm a mile off, I was unsure if rule 3 was correct to apply for the 2nd part and if I have used it correctly?!)

Derivative of cosine is - sine and you already have a minus sign, so...? Also what about the "derivative of the inside" (chain rule) in the second term.
Also note that generally this forum wants separate problems listed in separate threads.

 

[Brinkley23]

Derivative of cosine is - sine and you already have a minus sign, so...? Also what about the "derivative of the inside" (chain rule) in the second term.
Also note that generally this forum wants separate problems listed in separate threads.

My apologies, I will create a new separate thread for this question, especially as you've just thrown a new rule at me (chain rule) I don't have this in my notes that have been given to me, so I'll need to do some further reading up. Thanks for all your help, I really appreciate it

 

[Dr.Peterson]

oh and seeing as I've got you... (last one I promise)

y= 6sin3x - cos2x

My working out using rule 2: na cos ax and 3: -na sin ax

dy/dx = 18cos3x -sin2x ? (I'm sure with this one I'm a mile off, I was unsure if rule 3 was correct to apply for the 2nd part and if I have used it correctly?!)

My apologies, I will create a new separate thread for this question, especially as you've just thrown a new rule at me (chain rule) I don't have this in my notes that have been given to me, so I'll need to do some further reading up. Thanks for all your help, I really appreciate it

The chain rule is implicit in the "rules" you stated; that is, these rules incorporate it (by multiplying by a) without you having to know about it explicitly. So you don't need to study anything new (yet). Once you learn the real rules, you won't need to memorize such specific rules for individual facts (though it will become automatic).

The point is that you failed to follow your rule for the second term. What happened to the "a", namely the 2?

By the way, when you state your rule, you should state it completely: the derivative of n cos(ax) is -na cos(ax). When you state just the derivative without saying what function it is for, you are inviting misunderstanding. We don't know what you mean by n unless you tell us.

 

[Steven G]

Please don't state rule numbers as they are teacher dependent and not universal.

 

[Brinkley23]

Please don't state rule numbers as they are teacher dependent and not universal.

Sorry, I didn't realise this.

 

[JeffM]

Sorry, I didn't realise this.

There are names for them that are relatively standard in the English speaking world.

The constant rule, which applies to constants
The sum rule, which applies to sums and differences
The product rule, which applies to products
The power rule, which applies to constant exponents
The quotient rule, which applies to quotients and is a special case of the product and power rules

And there is one rule "binds" them all: the chain rule.

Plus you need to know the sine rule and a few others.

Everything else is just combining the rules.

 

[Brinkley23]

There are names for them that are relatively standard in the English speaking world.

The constant rule, which applies to constants
The sum rule, which applies to sums and differences
The product rule, which applies to products
The power rule, which applies to constant exponents
The quotient rule, which applies to quotients and is a special case of the product and power rules

And there is one rule "binds" them all: the chain rule.

Plus you need to know the sine rule and a few others.

Everything else is just combining the rules.

Thanks JeffM, you may be glad to know (plus the rest of the people that have helped me on here) that I don't have any links to the maths profession, nor do I plan to.? I appreciate everyones time when assisting me with these basic (not to me!) equations.