What is the derivative of x^{10x} ?

The derivative of x^{10x} is 10x^{10x}(ln(x)+1)

What is the first derivative of x^{10x} ?

The first derivative of x^{10x} is 10x^{10x}(ln(x)+1)

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derivative of

x^{10 x}

10 x^{10 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{10 x})

Apply exponent rule:

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

x^{10 x} = e^{10 x l n (x)}

= \frac{d}{d x} (e^{10 x l n (x)})

Apply the chain rule:

e^{10 x l n (x)} \frac{d}{d x} (10 x ln (x))

= e^{10 x l n (x)} \frac{d}{d x} (10 x ln (x))

\frac{d}{d x} (10 x ln (x)) = 10 (ln (x) + 1)

= e^{10 x l n (x)} \cdot 10 (ln (x) + 1)

e^{10 x l n (x)} = x^{10 x}

= 10 x^{10 x} (ln (x) + 1)

What is the derivative of x^{10x} ?
The derivative of x^{10x} is 10x^{10x}(ln(x)+1)
What is the first derivative of x^{10x} ?
The first derivative of x^{10x} is 10x^{10x}(ln(x)+1)