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Problem For x > 0 x>0 x > 0 p ( x ) = e 2 x ln ( 5 x ) log 3 x p(x)=\dfrac{e^{2x}\,\ln(5x)}{\log_{3}x} p ( x ) = log 3 x e 2 x ln ( 5 x ) p ′ ( x ) p'(x) p ′ ( x ) ( 2 e 2 x ln ( 5 x ) + e 2 x x ) ln x ln 3 + e 2 x ln ( 5 x ) x ln 3 ( ln x ln 3 ) 2 \displaystyle \frac{\left(2e^{2x}\ln(5x)+\dfrac{e^{2x}}{x}\right)\dfrac{\ln x}{\ln 3}+\dfrac{e^{2x}\ln(5x)}{x\ln 3}}{\left(\dfrac{\ln x}{\ln 3}\right)^{2}} ( ln 3 ln x ) 2 ( 2 e 2 x ln ( 5 x ) + x e 2 x ) ln 3 ln x + x ln 3 e 2 x ln ( 5 x ) ( 2 e 2 x ln ( 5 x ) + e 2 x x ) ln x ln 3 − e 2 x ln ( 5 x ) x ( ln x ln 3 ) 2 \displaystyle \frac{\left(2e^{2x}\ln(5x)+\dfrac{e^{2x}}{x}\right)\dfrac{\ln x}{\ln 3}-\dfrac{e^{2x}\ln(5x)}{x}}{\left(\dfrac{\ln x}{\ln 3}\right)^{2}} ( ln 3 ln x ) 2 ( 2 e 2 x ln ( 5 x ) + x e 2 x ) ln 3 ln x − x e 2 x ln ( 5 x ) ( 2 e 2 x ln ( 5 x ) + e 2 x x ) ln x ln 3 − e 2 x ln ( 5 x ) x ln 3 ( ln x ln 3 ) 2 \displaystyle \frac{\left(2e^{2x}\ln(5x)+\dfrac{e^{2x}}{x}\right)\dfrac{\ln x}{\ln 3}-\dfrac{e^{2x}\ln(5x)}{x\ln 3}}{\left(\dfrac{\ln x}{\ln 3}\right)^{2}} ( ln 3 ln x ) 2 ( 2 e 2 x ln ( 5 x ) + x e 2 x ) ln 3 ln x − x ln 3 e 2 x ln ( 5 x ) ( 2 e 2 x ln ( 5 x ) − e 2 x x ) ln x ln 3 − e 2 x ln ( 5 x ) x ln 3 ( ln x ln 3 ) 2 \displaystyle \frac{\left(2e^{2x}\ln(5x)-\dfrac{e^{2x}}{x}\right)\dfrac{\ln x}{\ln 3}-\dfrac{e^{2x}\ln(5x)}{x\ln 3}}{\left(\dfrac{\ln x}{\ln 3}\right)^{2}} ( ln 3 ln x ) 2 ( 2 e 2 x ln ( 5 x ) − x e 2 x ) ln 3 ln x − x ln 3 e 2 x ln ( 5 x ) Browse the problem library