Question

Найти производные функций: а) y=Sinx/Inx; y=e^x^2; y=x^2Inx

Answer 1

Ответ:

a) y' = (sin(x)/ln(x))' = (x * log(x) * cos(x) - sin(x))/(x*log^2(x))

b) y' = (e^x^2)' = 2 * e^x^2 * x

c) y' = (x^2*In(x))' = x + 2 * x * log(x)

Пошаговое объяснение:

a) y' = (sin(x)/ln(x))' = (cos(x)/ log(x)) - (sin(x)/x*log^2(x)) = (x * log(x) * cos(x) - sin(x))/(x*log^2(x))

b) y' = (e^x^2)' = 2 * e^x^2 * x

c) y' = (x^2*In(x))' = x * (2*log(x) + 1) = x + 2 * x * log(x)

Answer 2

$1)\; \; y=\frac{sinx}{lnx}\\\\y'=\frac{cosx\cdot lnx-sinx\cdot \frac{1}{x}}{ln^2x}=\frac{x\cdot cosx\cdot lnx-sinx}{x\cdot ln^2x}\\\\2)\;\; y=e^{x^2}\\\\y'=e^{x^2}\cdot 2x\\\\3)\; \; y=x^2\cdot lnx\\\\y'=2x\cdot lnx+x^2\cdot \frac{1}{x}=2x\cdot lnx+x=x\cdot (2\, lnx+1)$