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How do you find the derivative of #f(x) = (5x^2 + 11)e^(-21x)#?

Answer 1

Aurora Alvarado

#f'(x)=-21*(5x^2 + 11)*e^(-21x)+(10x)*e^(-21x)#

display below

#f(x) = (5x^2 + 11)*e^(-21x)#

#f'(x)=(5x^2 + 11)*-21*e^(-21x)+e^(-21x)*(10x)#

#f'(x)=-21*(5x^2 + 11)*e^(-21x)+(10x)*e^(-21x)#

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Answer 2

Axel Alvarez

To find the derivative of ( f(x) = (5x^2 + 11)e^{-21x} ), you can use the product rule of differentiation, which states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

So, let ( u = 5x^2 + 11 ) and ( v = e^{-21x} ). Then, ( u' = 10x ) (derivative of ( u ) with respect to ( x )) and ( v' = -21e^{-21x} ) (derivative of ( v ) with respect to ( x )).

Now, using the product rule, the derivative of ( f(x) ) is:

[ f'(x) = u'v + uv' ]

[ f'(x) = (10x)(e^{-21x}) + (5x^2 + 11)(-21e^{-21x}) ]

[ f'(x) = 10xe^{-21x} - 105x^2e^{-21x} - 231e^{-21x} ]

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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.