Differentiate 5cos(3x+1)

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Differentiate 5cos(3x+1)

Aug 3rd, 2015

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)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 3rd, 2015

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?

Aug 3rd, 2015

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)

= -15sin(3x+1)

hope that clears it up

Aug 3rd, 2015

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