What is the derivative of 7/(xln(x)) ?

The derivative of 7/(xln(x)) is -(7(ln(x)+1))/(x^2ln^2(x))

What is the first derivative of 7/(xln(x)) ?

The first derivative of 7/(xln(x)) is -(7(ln(x)+1))/(x^2ln^2(x))

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\frac{d}{d x} (\frac{7}{x ln ( x )})

- \frac{7 ( ln ( x ) + 1 )}{x ^{2} ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{7}{x ln ( x )})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{1}{x ln ( x )})

Apply exponent rule:

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

= 7 \frac{d}{d x} ((x ln (x))^{- 1})

Apply the chain rule:

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

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

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

= 7 (- \frac{1}{( x ln ( x ) ) ^{2}} (ln (x) + 1))

Simplify

7 (- \frac{1}{( x ln ( x ) ) ^{2}} (ln (x) + 1)) : - \frac{7 ( ln ( x ) + 1 )}{x ^{2} ln ^{2} ( x )}

= - \frac{7 ( ln ( x ) + 1 )}{x ^{2} ln ^{2} ( x )}

\frac{\partial}{\partial y} (x^{2} + z^{2})

\frac{\partial}{\partial x} (a)

f (x) = (\frac{( x - 3 )}{( x + 2 )})^{2} x = - 1

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{3}} d x

y^{^{'}} = ry (1 - \frac{y}{k})

What is the derivative of 7/(xln(x)) ?
The derivative of 7/(xln(x)) is -(7(ln(x)+1))/(x^2ln^2(x))
What is the first derivative of 7/(xln(x)) ?
The first derivative of 7/(xln(x)) is -(7(ln(x)+1))/(x^2ln^2(x))