What is implicit (dy)/(dx),y=x^x ?

The answer to implicit (dy)/(dx),y=x^x is (dy)/(dx)=x^x(ln(x)+1)

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implicit (dy)/(dx),y=x^x

implicit derivative

\frac{d y}{d x}, y = x^{x}

\frac{d y}{d x} = x^{x} (ln (x) + 1)

Solution steps

y = x^{x}

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = x^{x} (ln (x) + 1)

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = x^{x} (ln (x) + 1)

\frac{d y}{d x} = x^{x} (ln (x) + 1)

x \to 1 lim (\frac{11 x ^{2} - 99}{x ^{2} - 20 x + 51})

1.5 cos (\frac{2 π}{25} x)

2 t

\int sin (y^{2}) d y

x \to 0 lim (\frac{e ^{x} - 1}{20 x})

What is implicit (dy)/(dx),y=x^x ?
The answer to implicit (dy)/(dx),y=x^x is (dy)/(dx)=x^x(ln(x)+1)