derive Y =e ^tan(ln(sinx))
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Bom dia!
Derivando:
![<br />y=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\left[{\tan\left(\ln\left(\sin{x}\right)\right)}\right]'\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\left(\ln\left(\sin{x}\right)\right)'\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\sin{x}}\cdot\left(\sin{x}\right)'\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\sin{x}}\cdot\cos{x}\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\tan{x}}<br />](https://tex.z-dn.net/?f=%3Cbr+%2F%3Ey%3De%5E%7B%5Ctan%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5C%5C%3Cbr+%2F%3Ey%27%3De%5E%7B%5Ctan%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cleft%5B%7B%5Ctan%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Cright%5D%27%5C%5C%3Cbr+%2F%3Ey%27%3De%5E%7B%5Ctan%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cfrac%7B1%7D%7B%5Ccos%5E2%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%27%5C%5C%3Cbr+%2F%3Ey%27%3De%5E%7B%5Ctan%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cfrac%7B1%7D%7B%5Ccos%5E2%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cfrac%7B1%7D%7B%5Csin%7Bx%7D%7D%5Ccdot%5Cleft%28%5Csin%7Bx%7D%5Cright%29%27%5C%5C%3Cbr+%2F%3Ey%27%3De%5E%7B%5Ctan%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cfrac%7B1%7D%7B%5Ccos%5E2%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cfrac%7B1%7D%7B%5Csin%7Bx%7D%7D%5Ccdot%5Ccos%7Bx%7D%5C%5C%3Cbr+%2F%3Ey%27%3De%5E%7B%5Ctan%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cfrac%7B1%7D%7B%5Ccos%5E2%5Cleft%28%5Cln%5Cleft%28%5Csin%7Bx%7D%5Cright%29%5Cright%29%7D%5Ccdot%5Cfrac%7B1%7D%7B%5Ctan%7Bx%7D%7D%3Cbr+%2F%3E "<br />y=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\left[{\tan\left(\ln\left(\sin{x}\right)\right)}\right]'\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\left(\ln\left(\sin{x}\right)\right)'\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\sin{x}}\cdot\left(\sin{x}\right)'\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\sin{x}}\cdot\cos{x}\\<br />y'=e^{\tan\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\cos^2\left(\ln\left(\sin{x}\right)\right)}\cdot\frac{1}{\tan{x}}<br />")
Espero ter ajudado!
Derivando:
Espero ter ajudado!
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