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

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

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

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

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derivative of

y = \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 )}

3 \frac{d ^{2} y}{d x ^{2}} + 18 \frac{d y}{d x} + 24 y = 6 sin (2 x)

\int 12 e^{6 x} d x

\frac{1}{3 + 2 x}

\int (x^{4} + x^{2})^{8} (4 x^{3} + 2 x) d x

y^{^{''}} + 4 y = sin (2 x) cos (2 x)

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