anonymous
  • anonymous
???
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\(f(x) = (x+2)^{7x}\) , right?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
so, \(y= (x+2)^{7x}\) ln both sides, what do you get?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
What do you mean?
anonymous
  • anonymous
\(ln\), or log .
anonymous
  • anonymous
I did chain rule and got 7x(x+2)^(6x)
anonymous
  • anonymous
No way!! this is an exponent function with variable on the exponent. You use chain rule if the exponent is a constant. Only one way to take the exponent down is take \(ln\) both sides and use implicit derivative to find dy/dx.
anonymous
  • anonymous
Im not sure how to do that
anonymous
  • anonymous
ok, I do it for you as sample \(ln y = 7x ln(x+2)\) Now take derivative both sides \(\dfrac{y'}{y}= 7ln(x+2) +\dfrac{7x}{x+2}\) multiple y both sides, and replace \(y = (x+2)^{7x}\) , you get the answer
anonymous
  • anonymous
Okay so it would be (7ln(x+2) + 7x/(x+2))(x+2)^7x
phi
  • phi
yes
anonymous
  • anonymous
Thank you!!
phi
  • phi
oops used implicit differentiation another way is to use this factoid (by definition): \[ x= e^{\ln x } \] use that to say \[ (x+2)= e^{\ln(x+2)} \] and \[ (x+2)^{7x}= \left(e^{\ln(x+2)} \right)^{7x} \\y= e^{7x\ln(x+2)} \] now you can take the deriviative
anonymous
  • anonymous
Thank you so much @phi !!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.