What is the derivative of f(x)=(2-ln(x^2))/(x^2) ?

The derivative of f(x)=(2-ln(x^2))/(x^2) is -(2(-ln(x^2)+3))/(x^3)

What is the first derivative of f(x)=(2-ln(x^2))/(x^2) ?

The first derivative of f(x)=(2-ln(x^2))/(x^2) is -(2(-ln(x^2)+3))/(x^3)

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derivative of

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

- \frac{2 ( - ln ( x ^{2} ) + 3 )}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - \frac{2}{x} ) x ^{2} - 2 x ( 2 - ln ( x ^{2} ) )}{( x ^{2} ) ^{2}} : - \frac{2 ( - ln ( x ^{2} ) + 3 )}{x ^{3}}

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

n = 1, 3, 5 \sum \infty \frac{1}{n ^{2}}

f (x) = \frac{5 x}{x + 4}, (1, 1)

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

x \to 2 lim (\frac{( 3 x + 2 )}{5 x - 2})^{\frac{( 3 )}{x - 2}}

\int (x - 2) 2 d x

What is the derivative of f(x)=(2-ln(x^2))/(x^2) ?
The derivative of f(x)=(2-ln(x^2))/(x^2) is -(2(-ln(x^2)+3))/(x^3)
What is the first derivative of f(x)=(2-ln(x^2))/(x^2) ?
The first derivative of f(x)=(2-ln(x^2))/(x^2) is -(2(-ln(x^2)+3))/(x^3)