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How do you use the chain rule to differentiate #-cos(4x+9)#?

Answer 1

Christopher Allers

#4sin(4x+9)#

Using the chain rule and let #u=4x+9#

#d/(du)(-cosu)*d/(du)(u)#

#d/(du)(-cosu)=sinu#

#d/(dx)4x+9=4#

Therefore the answer is,

#d/dx(-cos(4x+9))=4sin(4x+9)#

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Answer 2

Adam Adkins

To differentiate -cos(4x+9) using the chain rule:

Identify the outer function as cosine and the inner function as 4x+9.
Take the derivative of the outer function, which is -sin(4x+9).
Multiply this by the derivative of the inner function, which is 4.
Combine the results to get the final derivative: -4sin(4x+9).

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