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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{v}{2}

15 x^{100} - 3 x^{12} + 5 x - 46

\frac{- 6}{x}

(4 x^{3} - 5 x^{2} + 1)^{4}

y = (\frac{x + 1}{x})^{2}

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