anonymous
  • anonymous
if y = (sin x)^x^2 then differentiate this!!!!! Pls give full steps!!!!!!
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.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
chane rule
anonymous
  • anonymous
use d f(x)^g(x)/ dx = f(x)^g(x)d/dx(g(x)log(f(x)) This can be proved easily
anonymous
  • anonymous
=cos x *2x

Looking for something else?

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

More answers

anonymous
  • anonymous
so here i gotta apply the chain rule got it so i have to learn it keep answering ppl i will just go through and then maybe I will be able to understand the solution!!!!
anonymous
  • anonymous
keep posting what you do!
anonymous
  • anonymous
ok
anonymous
  • anonymous
@ruba: not you, I was telling that to tejeshwar so that he may understand and we may correct him if you are wrong
anonymous
  • anonymous
Tejeshwar: this is not exaclty chain rule, f(x)^g(x) is a bit different thing
anonymous
  • anonymous
nope sure its chain rule
anonymous
  • anonymous
First take y=sin(x)^x^2 log(y)=x^2log(sinx) d/dx on both sides so you get, 1/y dy/dx = d/dx (x^2log(sinx)) therefore, dy/dx=y d/dx(x^2log(sin(x))
anonymous
  • anonymous
\[sin(x)^{x^2}\]?
anonymous
  • anonymous
ohhhhhhh so so so s o sry mogh im jst 4geting this
anonymous
  • anonymous
if so take the log, simplify, take the derivative, then multiply by \[sin(x)^{x^2}\]
anonymous
  • anonymous
ri8 ri8 sat & mogh go on nd bye
anonymous
  • anonymous
Take this into consideration, y = f(x)^g(x) log y = g(x) log(f(x)) \[(1/y)dy/dx = d/dx(g(x)\log(f(x)))\]
anonymous
  • anonymous
\[ln(sin(x)^{x^2})=x^2ln(sin(x))\] \[\frac{d}{dx}x^2ln(sin(x))=2xln(sin(x))+\frac{x^2}{x}=2xln(sin(x))+x\] answer: \[(sin(x))^{x^2}(2xln(sin(x))+x)\]
anonymous
  • anonymous
oops sorry wrong
anonymous
  • anonymous
\[\frac{d}{dx}x^2ln(sin(x))=2xln(sin(x))+\frac{x^2}{sin(x)}\]
anonymous
  • anonymous
my mistake. sorry.
anonymous
  • anonymous
@satellite: d/dx ln(sin(x)) is \[cosx/sinx\]
anonymous
  • anonymous
wow am i off . you are right and i am wrong!
anonymous
  • anonymous
two mistakes in one post i should resign.
anonymous
  • anonymous
lol, it happens!
anonymous
  • anonymous
btw it is also correct two write \[(sin(x))^{x^2}=e^{x^2ln(sin(x))}\] and differentiate this using the chain rule. the actual work is identical since it all boils down to finding the derivative of \[x^2ln(sin(x))\]CORRECTLY
anonymous
  • anonymous
just hang on satellite i will just be back 1ce i understand the chain rule!!!!
anonymous
  • anonymous
Chain rule is easier than it looks, just check out the proof too! Regards.

Looking for something else?

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