What is the derivative of (8x)^{ln(8x)} ?

The derivative of (8x)^{ln(8x)} is (2e^{ln^2(8x)}ln(8x))/x

What is the first derivative of (8x)^{ln(8x)} ?

The first derivative of (8x)^{ln(8x)} is (2e^{ln^2(8x)}ln(8x))/x

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derivative of

(8 x)^{l n (8 x)}

\frac{2 e ^{l n^{2} (8 x)} ln ( 8 x )}{x}

Solution steps

\frac{d}{d x} ((8 x)^{l n (8 x)})

Apply exponent rule:

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

(8 x)^{l n (8 x)} = e^{l n (8 x) l n (8 x)}

= \frac{d}{d x} (e^{l n (8 x) l n (8 x)})

Apply the chain rule:

e^{l n (8 x) l n (8 x)} \frac{d}{d x} (ln (8 x) ln (8 x))

= e^{l n (8 x) l n (8 x)} \frac{d}{d x} (ln (8 x) ln (8 x))

\frac{d}{d x} (ln (8 x) ln (8 x)) = \frac{2 ln ( 8 x )}{x}

= e^{l n (8 x) l n (8 x)} \frac{2 ln ( 8 x )}{x}

Simplify

e^{l n (8 x) l n (8 x)} \frac{2 ln ( 8 x )}{x} : \frac{2 e ^{l n^{2} (8 x)} ln ( 8 x )}{x}

= \frac{2 e ^{l n^{2} (8 x)} ln ( 8 x )}{x}

\frac{d}{d x} (\frac{ln ( x )}{x ^{3}})

x \to 0 lim (arcsin (x))

7 x^{4} arctan (2 x^{3})

y^{^{'}} = 2 x y + x

\frac{d}{d x} ((2 x - 1)^{\frac{3}{2}})

What is the derivative of (8x)^{ln(8x)} ?
The derivative of (8x)^{ln(8x)} is (2e^{ln^2(8x)}ln(8x))/x
What is the first derivative of (8x)^{ln(8x)} ?
The first derivative of (8x)^{ln(8x)} is (2e^{ln^2(8x)}ln(8x))/x