What is the derivative of x^{7x} ?

The derivative of x^{7x} is 7x^{7x}(ln(x)+1)

What is the first derivative of x^{7x} ?

The first derivative of x^{7x} is 7x^{7x}(ln(x)+1)

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derivative of

x^{7 x}

7 x^{7 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{7 x})

Apply exponent rule:

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

x^{7 x} = e^{7 x l n (x)}

= \frac{d}{d x} (e^{7 x l n (x)})

Apply the chain rule:

e^{7 x l n (x)} \frac{d}{d x} (7 x ln (x))

= e^{7 x l n (x)} \frac{d}{d x} (7 x ln (x))

\frac{d}{d x} (7 x ln (x)) = 7 (ln (x) + 1)

= e^{7 x l n (x)} \cdot 7 (ln (x) + 1)

e^{7 x l n (x)} = x^{7 x}

= 7 x^{7 x} (ln (x) + 1)

What is the derivative of x^{7x} ?
The derivative of x^{7x} is 7x^{7x}(ln(x)+1)
What is the first derivative of x^{7x} ?
The first derivative of x^{7x} is 7x^{7x}(ln(x)+1)