Home > Calculus > Product Rule

How do you differentiate #g(x) = cos(5x) (x^2-4)# using the product rule?

Answer 1

Scarlett Allison

#g^(')(x) = -5sin(5x)(x^2-4) + cos(5x)(2x)#

#g(x) = cos(5x)(x^2-4)#

Product guideline

Applied:

#g^(')(x) = -5sin(5x)(x^2-4) + cos(5x)(2x)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Aurora Alvarado

To differentiate g(x) = cos(5x) (x^2-4) using the product rule, you need to apply the rule which states that the derivative of the product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

So, the derivative of g(x) = cos(5x) (x^2-4) using the product rule would be:

g'(x) = (cos(5x) * (2x)) + ((x^2-4) * (-5sin(5x)))

Therefore, g'(x) = 2x cos(5x) - 5sin(5x) (x^2-4).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.