What is the derivative of (x^x)^3 ?

The derivative of (x^x)^3 is 3x^{3x}(ln(x)+1)

What is the first derivative of (x^x)^3 ?

The first derivative of (x^x)^3 is 3x^{3x}(ln(x)+1)

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derivative of

(x^{x})^{3}

3 x^{3 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} ((x^{x})^{3})

Simplify

(x^{x})^{3} : x^{3 x}

= \frac{d}{d x} (x^{3 x})

Apply exponent rule:

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

x^{3 x} = e^{3 x l n (x)}

= \frac{d}{d x} (e^{3 x l n (x)})

Apply the chain rule:

e^{3 x l n (x)} \frac{d}{d x} (3 x ln (x))

= e^{3 x l n (x)} \frac{d}{d x} (3 x ln (x))

\frac{d}{d x} (3 x ln (x)) = 3 (ln (x) + 1)

= e^{3 x l n (x)} \cdot 3 (ln (x) + 1)

e^{3 x l n (x)} = x^{3 x}

= 3 x^{3 x} (ln (x) + 1)

\frac{x}{x ^{3} + 1}

\frac{d}{d n} ((- i)^{4 n})

\frac{y ^{2}}{x ^{2}}

a^{3} - 3

y = (x^{2} - 4) (2 x - 6)

What is the derivative of (x^x)^3 ?
The derivative of (x^x)^3 is 3x^{3x}(ln(x)+1)
What is the first derivative of (x^x)^3 ?
The first derivative of (x^x)^3 is 3x^{3x}(ln(x)+1)