What is the derivative of ({f}(x)/(x^2)) ?

The derivative of ({f}(x)/(x^2)) is (x derivative of {f}(x)-2{f}(x))/(x^3)

What is the first derivative of ({f}(x)/(x^2)) ?

The first derivative of ({f}(x)/(x^2)) is (x derivative of {f}(x)-2{f}(x))/(x^3)

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

\frac{x \frac{d}{d x} ( f ( x ) ) - 2 f ( x )}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Simplify

\frac{\frac{d}{d x} ( f ( x ) ) x ^{2} - 2 x f ( x )}{( x ^{2} ) ^{2}} : \frac{x \frac{d}{d x} ( f ( x ) ) - 2 f ( x )}{x ^{3}}

= \frac{x \frac{d}{d x} ( f ( x ) ) - 2 f ( x )}{x ^{3}}

What is the derivative of ({f}(x)/(x^2)) ?
The derivative of ({f}(x)/(x^2)) is (x derivative of {f}(x)-2{f}(x))/(x^3)
What is the first derivative of ({f}(x)/(x^2)) ?
The first derivative of ({f}(x)/(x^2)) is (x derivative of {f}(x)-2{f}(x))/(x^3)