What is the derivative of-(x^{ln(x})/6) ?

The derivative of-(x^{ln(x})/6) is -(e^{ln^2(x)}ln(x))/(3x)

What is the first derivative of-(x^{ln(x})/6) ?

The first derivative of-(x^{ln(x})/6) is -(e^{ln^2(x)}ln(x))/(3x)

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\frac{d}{d x} (- \frac{x ^{l n (x)}}{6})

- \frac{e ^{l n^{2} (x)} ln ( x )}{3 x}

Solution steps

\frac{d}{d x} (- \frac{x ^{l n (x)}}{6})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{6} \frac{d}{d x} (x^{l n (x)})

Apply exponent rule:

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

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

= - \frac{1}{6} \frac{d}{d x} (e^{l n (x) l n (x)})

Apply the chain rule:

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

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

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

= - \frac{1}{6} e^{l n (x) l n (x)} \frac{2 ln ( x )}{x}

Simplify

- \frac{1}{6} e^{l n (x) l n (x)} \frac{2 ln ( x )}{x} : - \frac{e ^{l n^{2} (x)} ln ( x )}{3 x}

= - \frac{e ^{l n^{2} (x)} ln ( x )}{3 x}

f (x) = x^{2} - 4 x, g (x) = 0

\frac{d}{d x} ((5 x^{7} - 7 x^{5} + 12) (3 x^{6} - 2 x))

x \to 1 lim (x + 3)

(x^{3} + 2)^{5}

What is the derivative of-(x^{ln(x})/6) ?
The derivative of-(x^{ln(x})/6) is -(e^{ln^2(x)}ln(x))/(3x)
What is the first derivative of-(x^{ln(x})/6) ?
The first derivative of-(x^{ln(x})/6) is -(e^{ln^2(x)}ln(x))/(3x)