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Popular >

derivative of y=x^{9x}

Solution

derivative of

y = x^{9 x}

Solution

9 x^{9 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{9 x})

Apply exponent rule:

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

x^{9 x} = e^{9 x l n (x)}

= \frac{d}{d x} (e^{9 x l n (x)})

Apply the chain rule:

e^{9 x l n (x)} \frac{d}{d x} (9 x ln (x))

= e^{9 x l n (x)} \frac{d}{d x} (9 x ln (x))

\frac{d}{d x} (9 x ln (x)) = 9 (ln (x) + 1)

= e^{9 x l n (x)} \cdot 9 (ln (x) + 1)

e^{9 x l n (x)} = x^{9 x}

= 9 x^{9 x} (ln (x) + 1)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^{9x} ?
The derivative of y=x^{9x} is 9x^{9x}(ln(x)+1)
What is the first derivative of y=x^{9x} ?
The first derivative of y=x^{9x} is 9x^{9x}(ln(x)+1)