What is the derivative of x^{x+2} ?

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

What is the first derivative of x^{x+2} ?

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

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derivative of

x^{x + 2}

x^{x + 2} (ln (x) + \frac{x + 2}{x})

Solution steps

\frac{d}{d x} (x^{x + 2})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{x + 2} = e^{(x + 2) l n (x)}

= \frac{d}{d x} (e^{(x + 2) l n (x)})

Apply the chain rule:

e^{(x + 2) l n (x)} \frac{d}{d x} ((x + 2) ln (x))

= e^{(x + 2) l n (x)} \frac{d}{d x} ((x + 2) ln (x))

\frac{d}{d x} ((x + 2) ln (x)) = ln (x) + \frac{x + 2}{x}

= e^{(x + 2) l n (x)} (ln (x) + \frac{x + 2}{x})

e^{(x + 2) l n (x)} = x^{x + 2}

= x^{x + 2} (ln (x) + \frac{x + 2}{x})

\frac{d}{d x} (\frac{x ^{2} - 64}{x - 8})

f (x) = 3 - x

x \to - 1 lim (π)

x \to - 9 lim (50)

\int \frac{1}{sec ( t ) + tan ( t )} d t

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