Differentiate 5cos(3x+1)

Thank you for the opportunity to help you with your question!

Use the chain rule:

d/dx(5cos(3x+1))(d/dx(3x+1)

= -5sin(3x+1)(3)

= -15sin(3x+1)

I am quite unsure with the chain rule. Firstly, how do you know identify which part to "split". In this case, you split cos(3x+1) into cos(3x+1) and (3x+1). Also, why is 5 negative?

first note that the derivative of cosx = -sinx, do you agree?

Then, the derivative of cos(anything) = -sin(anything) does that make sense?

But, additionally, according to the chain rule, you must also differentiate the variable of the function which in this case is 3x+1

the derivative of 3x+1 = 3 do you agree?

Then, according to the chain rule, that part is multiplied with the original derivative:

So, the derivative of 5cos(3x+1) = 5*(-sin(3x+1))*(3)

hope that clears it up

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