What is the derivative of f(x)= 6/(ln(x)) ?

The derivative of f(x)= 6/(ln(x)) is -6/(xln^2(x))

What is the first derivative of f(x)= 6/(ln(x)) ?

The first derivative of f(x)= 6/(ln(x)) is -6/(xln^2(x))

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derivative of

f (x) = \frac{6}{ln ( x )}

- \frac{6}{x ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{6}{ln ( x )})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{1}{ln ( x )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= 6 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Simplify

6 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{6}{x ln ^{2} ( x )}

= - \frac{6}{x ln ^{2} ( x )}

\frac{d y}{d x} + \frac{3}{x} y = 16 y^{3}

\int_{4}^{7} \frac{x}{x ^{2} + 6 x + 13} d x

f (x) = 2 x^{2} + 2 x, at x = - 3

\int x e - x d x

What is the derivative of f(x)= 6/(ln(x)) ?
The derivative of f(x)= 6/(ln(x)) is -6/(xln^2(x))
What is the first derivative of f(x)= 6/(ln(x)) ?
The first derivative of f(x)= 6/(ln(x)) is -6/(xln^2(x))