What is the derivative of 3/(ln(x)) ?

The derivative of 3/(ln(x)) is -3/(xln^2(x))

What is the first derivative of 3/(ln(x)) ?

The first derivative of 3/(ln(x)) is -3/(xln^2(x))

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derivative of

\frac{3}{ln ( x )}

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

Solution steps

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

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{ln ( x )})

Apply exponent rule:

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

= 3 \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}

= 3 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Simplify

3 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{3}{x ln ^{2} ( x )}

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

x^{2} y^{^{''}} - x y^{^{'}} - 3 y = 0

\frac{x d y}{d x} = \frac{1}{y ^{3}}

\frac{d y}{d x} = (4 + 3 x)^{4}

\int e^{t x} \cdot \frac{1}{θ} e^{- \frac{x}{θ}} d x

x^{2} y^{^{''}} + 2 x y^{^{'}} - 6 y = 0

What is the derivative of 3/(ln(x)) ?
The derivative of 3/(ln(x)) is -3/(xln^2(x))
What is the first derivative of 3/(ln(x)) ?
The first derivative of 3/(ln(x)) is -3/(xln^2(x))