What is the derivative of 1/(log_{10)(x^2)} ?

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (lo g_{10} (x^{2})) = \frac{2}{ln ( 10 ) x}

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

Simplify

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

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

\frac{1 + t ^{2}}{4}

\frac{x cos ( x )}{1 + x ^{2}}

1 + w^{2}

2 (x sin (x) + cos (x))

\frac{1}{3 x ^{2} + 2}

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