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steel11
derivative of 2xsin(1/x) my answer i put, which is wrong 2sinx^-1*cosx^-1*-1x^-2 can anybody give me correct answer or find where i went wrong? im doing the chain rule, and i think you have to do twice, which i did. btw, i brought the x to the numerator with -1 as exponent.
do u know abut product derivation d\dx(a*b) = a d\dx(b) + b d\dx(a)
I would like to do this with chain rule. If thats possible, which I think it is.
try to use my method and tell me the answer u got
Let\[f(x)=2x\sin\left(\frac1x\right).\]Then\[f'(x)=2\sin\left(\frac1x\right)+2x\cos\left(\frac1x\right)\cdot\left(-\frac1{x^2}\right)=2\left[\sin\left(\frac1x\right)-\frac1x\cos\left(\frac1x\right)\right].\]
thank you across. you used product rule and chain rule to solve right?
guess uzumaki was right on having to use product rule. ._.
that what i am talking about thanx @across
Yes. To be more specific, let me break it down for you: Essentially, you have this:\[f(x)=g(x)h(j(x)),\]where\[g(x)=2x\\h(x)=\sin x\\j(x)=\frac1x.\]Then\[f'(x)=g'(x)h(j(x))+g(x)h'(j(x))j'(x),\]and since\[g'(x)=2\\h'(x)=\cos x\\j'(x)=-\frac1{x^2},\]we have that\[f'(x)=2\cos\left(\frac1x\right)+2x\cos\left(\frac1x\right)\cdot\left(\frac1{x^2}\right).\]
I forgot the negative sign in the last term, but you get the idea. I used the product and chain rules.