Practice problem
Find dydx\frac{dy}{dx}dxdy for eylnx=2y\sqrt{e^y\ln x}=2^yeylnx=2y
dydx=2ey−lnx2yln(2)eylnx−eylnx\frac{dy}{dx}=\frac{2e^y-\ln x}{2^{y}\ln(2)\sqrt{e^y\ln x}-e^y\ln x}dxdy=2yln(2)eylnx−eylnx2ey−lnx
dydx=eyx(2y+1ln(2)eylnx−eylnx)\frac{dy}{dx}=\frac{e^y}{x(2^{y+1}\ln(2)\sqrt{e^y\ln x}-e^y\ln x)}dxdy=x(2y+1ln(2)eylnx−eylnx)ey
dydx=ey+1xy(2y+1eylnx−2eylnx)\frac{dy}{dx}=\frac{e^{y+1}}{xy(2^{y+1}\sqrt{e^y\ln x}-2e^y\ln x)}dxdy=xy(2y+1eylnx−2eylnx)ey+1
dydx=lnx2y+1ln(2)eylnx−3lnx\frac{dy}{dx}=\frac{\ln x}{2^{y+1}\ln(2)\sqrt{e^y\ln x}-3\ln x}dxdy=2y+1ln(2)eylnx−3lnxlnx
Type a concept, like “slope” or “photosynthesis”.
