What is the derivative of 1/(xlog_{10)(x)} ?

The derivative of 1/(xlog_{10)(x)} is -(ln(x)+1)/(ln(10)x^2log_{10)(x)^2}

What is the first derivative of 1/(xlog_{10)(x)} ?

The first derivative of 1/(xlog_{10)(x)} is -(ln(x)+1)/(ln(10)x^2log_{10)(x)^2}

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derivative of

\frac{1}{x lo g _{10} ( x )}

- \frac{ln ( x ) + 1}{ln ( 10 ) x ^{2} lo g _{10} ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x lo g _{10} ( x )})

Apply exponent rule:

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

= \frac{d}{d x} ((x lo g_{10} (x))^{- 1})

Apply the chain rule:

- \frac{1}{( x lo g _{10} ( x ) ) ^{2}} \frac{d}{d x} (x lo g_{10} (x))

= - \frac{1}{( x lo g _{10} ( x ) ) ^{2}} \frac{d}{d x} (x lo g_{10} (x))

\frac{d}{d x} (x lo g_{10} (x)) = lo g_{10} (x) + \frac{1}{ln ( 10 )}

= - \frac{1}{( x lo g _{10} ( x ) ) ^{2}} (lo g_{10} (x) + \frac{1}{ln ( 10 )})

Simplify

- \frac{1}{( x lo g _{10} ( x ) ) ^{2}} (lo g_{10} (x) + \frac{1}{ln ( 10 )}) : - \frac{ln ( x ) + 1}{ln ( 10 ) x ^{2} lo g _{10} ( x ) ^{2}}

= - \frac{ln ( x ) + 1}{ln ( 10 ) x ^{2} lo g _{10} ( x ) ^{2}}

x^{3} - 3 x^{2}

sin (10 x) + cos (15 x)

x^{2} ∣ x ∣

sin (x \cdot 2 + 2 x + 3)

\frac{10}{( x + 5 ) ^{2}}

What is the derivative of 1/(xlog_{10)(x)} ?
The derivative of 1/(xlog_{10)(x)} is -(ln(x)+1)/(ln(10)x^2log_{10)(x)^2}
What is the first derivative of 1/(xlog_{10)(x)} ?
The first derivative of 1/(xlog_{10)(x)} is -(ln(x)+1)/(ln(10)x^2log_{10)(x)^2}