# How do you find the derivative of #5xe^(2x)#?

Use the product rule and the derivative of

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To find the derivative of ( 5xe^{2x} ), we can use the product rule. The product rule states that if you have two functions ( u(x) ) and ( v(x) ), then the derivative of their product ( u(x)v(x) ) is given by ( u'(x)v(x) + u(x)v'(x) ). Applying the product rule to ( 5xe^{2x} ), we have:

( u(x) = 5x ) and ( v(x) = e^{2x} )

( u'(x) = 5 ) and ( v'(x) = 2e^{2x} )

Now, using the product rule formula:

( \frac{d}{dx} (5xe^{2x}) = u'(x)v(x) + u(x)v'(x) )

( = (5)(e^{2x}) + (5x)(2e^{2x}) )

( = 5e^{2x} + 10xe^{2x} )

Therefore, the derivative of ( 5xe^{2x} ) is ( 5e^{2x} + 10xe^{2x} ).

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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.

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.

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.

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