What is the derivative of x^x(ln(x)+1) ?

The derivative of x^x(ln(x)+1) is x^x(ln(x)+1)^2+x^{x-1}

What is the first derivative of x^x(ln(x)+1) ?

The first derivative of x^x(ln(x)+1) is x^x(ln(x)+1)^2+x^{x-1}

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derivative of

x^{x} (ln (x) + 1)

x^{x} (ln (x) + 1)^{2} + x^{x - 1}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{x}, g = ln (x) + 1

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

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

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

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

Simplify

x^{x} (ln (x) + 1) (ln (x) + 1) + \frac{1}{x} x^{x} : x^{x} (ln (x) + 1)^{2} + x^{x - 1}

= x^{x} (ln (x) + 1)^{2} + x^{x - 1}

\int \frac{1}{x ^{3} x ^{2} - 1} d x

4 cos^{2} (x)

1 9^{x}

\int 5 t^{2} e^{\frac{t ^{3}}{3}} d t

\int \frac{5 x ^{2}}{e ^{x}} d x

What is the derivative of x^x(ln(x)+1) ?
The derivative of x^x(ln(x)+1) is x^x(ln(x)+1)^2+x^{x-1}
What is the first derivative of x^x(ln(x)+1) ?
The first derivative of x^x(ln(x)+1) is x^x(ln(x)+1)^2+x^{x-1}