anonymous
  • anonymous
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Mathematics
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anonymous
  • anonymous
Help!
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
|dw:1434556398011:dw| this is your question, right?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
alright so , take them separately first , f'(x) of e^x = e^x , and f'(x) of ln x = 1/x in the question, they gave e^(lnx) also , which is basically equal to x since the e and ln cancel out if you put them together in a function so what we are left with is f(x) = e^x + xlnx we know that f'(x) of e^x = e^x but for xlnx , since there are two functions being multiplied with each other, you use the product rule :
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anonymous
  • anonymous
for the product rule you take one function as u and the other as v, and use the laws of differentiation that I wrote above to solve it and get the final answer
anonymous
  • anonymous
give it a go, and tell me what answer you get, and ill further help you if it's wrong :)
anonymous
  • anonymous
Okay
anonymous
  • anonymous
Would it be 1-lnx?
anonymous
  • anonymous
nope, okay look : u=x , v=ln x du/dx = 1 and dv/dx = 1/x so if you substitute into the formula x(1/x) + 1(lnx) and simplify it further : 1+lnx
anonymous
  • anonymous
So it would be 1+lnx+e^x?
anonymous
  • anonymous
yup :)
anonymous
  • anonymous
Alright thank you so much!
anonymous
  • anonymous
np

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