What is the derivative of x^{3x} ?

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

What is the first derivative of x^{3x} ?

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

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derivative of

x^{3 x}

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

Solution steps

\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)

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