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

The derivative of ((1-log_{10}(x)))/((x^2)) is -(2ln(10)(-log_{10}(x)+1)+1)/(ln(10)x^3)

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

The first derivative of ((1-log_{10}(x)))/((x^2)) is -(2ln(10)(-log_{10}(x)+1)+1)/(ln(10)x^3)

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derivative of

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

- \frac{2 ln ( 10 ) ( - lo g _{10} ( x ) + 1 ) + 1}{ln ( 10 ) x ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

\frac{( - \frac{1}{l n ( 10 ) x} ) x ^{2} - 2 x ( 1 - lo g _{10} ( x ) )}{( x ^{2} ) ^{2}} : - \frac{2 ln ( 10 ) ( - lo g _{10} ( x ) + 1 ) + 1}{ln ( 10 ) x ^{3}}

= - \frac{2 ln ( 10 ) ( - lo g _{10} ( x ) + 1 ) + 1}{ln ( 10 ) x ^{3}}

x (ln (x))^{2}

(x^{10})^{x}

\frac{8 x ^{2}}{3}

(1 - tan^{2} (x)) 3 (1 - sec^{2} (x)) 4

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

What is the derivative of ((1-log_{10}(x)))/((x^2)) ?
The derivative of ((1-log_{10}(x)))/((x^2)) is -(2ln(10)(-log_{10}(x)+1)+1)/(ln(10)x^3)
What is the first derivative of ((1-log_{10}(x)))/((x^2)) ?
The first derivative of ((1-log_{10}(x)))/((x^2)) is -(2ln(10)(-log_{10}(x)+1)+1)/(ln(10)x^3)