What is (\partial)/(\partial x)(x^{3x}) ?

The answer to (\partial)/(\partial x)(x^{3x}) is 3x^{3x}(ln(x)+1)

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(\partial)/(\partial x)(x^{3x})

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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)

\int x (x^{3} - \frac{2}{x ^{2}} + 6) d x

x \to 0 lim (x^{2} - \frac{cos ( x )}{10000})

\frac{\partial}{\partial x} (ln (x + y^{3}) - z)

\int \frac{8 x ^{7}}{( x ^{8} + 1 ) ^{2}} d x

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

What is (\partial)/(\partial x)(x^{3x}) ?
The answer to (\partial)/(\partial x)(x^{3x}) is 3x^{3x}(ln(x)+1)