Help with derivative problem

[barryjstudent]

Hey guys, need help with a quick problem…..I may have done incorrectly but it might have meant the same thing.
I used the chain rule. And I think I needed to use the product rule

Find the derivative of
f(x)= e^x(1+x)

 

[BigBeachBanana]

To make the problem a little bit easier you can distribute first.
[math]f(x)= e^x(1+x)=e^x+xe^x[/math]Now, you don't have to use chain rules, but you learn both ways. Please share your attempts.

 

[barryjstudent]

To make the problem a little bit easier you can distribute first.
[math]f(x)= e^x(1+x)=e^x+xe^x[/math]Now, you don't have to use chain rules, but you learn both ways. Please share your attempts.

So I could have used the chain OR product rule? How do you mean so ? Thought had to be one or another

 

[BigBeachBanana]

So I could have used the chain OR product rule? How do you mean so ? Thought had to be one or another

In the original form where you posted, you are correct that you'd have to use both product and chain rules. But when you distribute, you no longer need to use the chain rule. Can you see the reason? Also, that's why I said you should practice how to do it both ways. Both approaches should give you the same result. Show us what your attempt is, and we can help you see where things went wrong.

 

[barryjstudent]

In the original form where you posted, you are correct that you have to use both product and chain rules. But when you distribute, you no longer need to use the chain rule. Can you see the reason? Also, that's why I said you practice how to do it both ways. Both approaches should give you the same result. Show us what your attempt is, and we can help you see where things went wrong.

I do and I don’t would you be able to show me how you would do this. Really stumped on this one

 

[BigBeachBanana]

I do and I don’t would you be able to show me how you would do this. Really stumped on this one

I'll show you a similar problem, hope you can apply the same process.
Find the derivative of [imath]f(x)=x^2(1+x)[/imath]
Observe that [imath]f(x)[/imath] is a product of 2 functions, let [imath]g(x)=x^2[/imath] and [imath]h(x)=(1+x)[/imath]. Now the product rule states that
[math]\frac{d}{dx}[g(x)h(x)]=g'(x)h(x)+g(x)h'(x)[/math]Compute [imath]g'(x)[/imath] and [imath]h'(x)[/imath]:
[imath]g'(x)=2x[/imath] and [imath]h'(x)=0+1=1[/imath]
Plug the values into the product rule equation:
[math]\frac{d}{dx}[g(x)h(x)]=\red{g'(x)}\blue{h(x)}+\orange{g(x)}\purple{h'(x)}=\red{2x}\blue{(1+x)}+\orange{x^2}\purple{(1)}=3x^2+2x[/math]

 

[Steven G]

To compute the derivative of (1+x) you really do not need to use the chain rule. You can, but it is over kill