Practice problem
Find the derivative of y=(sinx)lnxy=(\sin x)^{\ln x}y=(sinx)lnx
y′=(sinx)lnx(ln(sinx)x+lnx(cosx)sinx)y'=(\sin x)^{\ln x}\left(\frac{\ln(\sin x)}{x}+\frac{\ln x(\cos x)}{\sin x}\right)y′=(sinx)lnx(xln(sinx)+sinxlnx(cosx))
y′=(sinx)lnx(sinxx+lnx(cosx))y'=(\sin x)^{\ln x}\left(\frac{\sin x}{x}+\ln x(\cos x)\right)y′=(sinx)lnx(xsinx+lnx(cosx))
y′=ln(sinx)x+lnx(cosx)sinxy'=\frac{\ln(\sin x)}{x}+\frac{\ln x(\cos x)}{\sin x}y′=xln(sinx)+sinxlnx(cosx)
y′=(sinx)lnx[ln(sinx)+lnx(cosx)]y'=(\sin x)^{\ln x}[\ln(\sin x)+\ln x(\cos x)]y′=(sinx)lnx[ln(sinx)+lnx(cosx)]
Type a concept, like “slope” or “photosynthesis”.
