Help with differentiating with respect to x

[Brinkley23]

Hi all, can I please get some help with the following question:

Differentiate the following with respect to x

y= 6sin3x - cos2x

My working out using rule 2: na cos ax and 3: -na sin ax
where a=3 n=6
dy/dx = 18cos3x + sin2x (not sure how far away I am)

Im hoping I have the 1st term correct, but Im struggling with how to apply the correct rule to the 2nd term?

Many Thanks

 

[Deleted member 4993]

Hi all, can I please get some help with the following question:

Differentiate the following with respect to x

y= 6sin3x - cos2x

My working out using rule 2: na cos ax and 3: -na sin ax
where a=3 n=6
dy/dx = 18cos3x + sin2x (not sure how far away I am)

Im hoping I have the 1st term correct, but Im struggling with how to apply the correct rule to the 2nd term?

Many Thanks

Almost had it:

y= 6*sin(3*x) - cos(2*x)

dy/dx = 18*cos(3*x) + 2*sin(2*x)

for the second term you had:

a = 1 and n = 2 ....\(\displaystyle \to \ \ \ \) n * a = 2

 

[Brinkley23]

Almost had it:

y= 6*sin(3*x) - cos(2*x)

dy/dx = 18*cos(3*x) + 2*sin(2*x)

for the second term you had:

a = 1 and n = 2 ....\(\displaystyle \to \ \ \ \) n * a = 2

Thanks for replying,

Just so that I feel I understand this more, the rule to be used in the 2nd term I know as -na sin ax (differentiated function), is it also correct if a=2 and n=1?

The reason I ask this is because the material I am referring to states ' rule 3: function Y = n cos ax '

Applying this to the 2nd term would n=1 and a=2? or am I really just confusing myself?

Sorry for my silly questions!

 

[Steven G]

The derivative of cos(anything) is -sin(anything)*(anything)'

 

[Dr.Peterson]

Thanks for replying,

Just so that I feel I understand this more, the rule to be used in the 2nd term I know as -na sin ax (differentiated function), is it also correct if a=2 and n=1?

The reason I ask this is because the material I am referring to states ' rule 3: function Y = n cos ax '

Applying this to the 2nd term would n=1 and a=2? or am I really just confusing myself?

Sorry for my silly questions!

Yes, a=2; and you can take n as either 1 or -1, depending on how you are viewing the term.

But the derivative of cos(2x) is -2sin(2x), not -sin(2x), because your rule says it is -na sin(ax), not just -n sin(ax).

You handled the "a" correctly in the first term; why not here too?