What is the derivative of ({f}(x)/(x^9)) ?

The derivative of ({f}(x)/(x^9)) is (x derivative of {f}(x)-9{f}(x))/(x^{10)}

What is the first derivative of ({f}(x)/(x^9)) ?

The first derivative of ({f}(x)/(x^9)) is (x derivative of {f}(x)-9{f}(x))/(x^{10)}

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\frac{d}{d x} (\frac{f ( x )}{x ^{9}})

\frac{x \frac{d}{d x} ( f ( x ) ) - 9 f ( x )}{x ^{10}}

Solution steps

\frac{d}{d x} (\frac{f ( x )}{x ^{9}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( f ( x ) ) x ^{9} - \frac{d}{d x} ( x ^{9} ) f ( x )}{( x ^{9} ) ^{2}}

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{\frac{d}{d x} ( f ( x ) ) x ^{9} - 9 x ^{8} f ( x )}{( x ^{9} ) ^{2}}

Simplify

\frac{\frac{d}{d x} ( f ( x ) ) x ^{9} - 9 x ^{8} f ( x )}{( x ^{9} ) ^{2}} : \frac{x \frac{d}{d x} ( f ( x ) ) - 9 f ( x )}{x ^{10}}

= \frac{x \frac{d}{d x} ( f ( x ) ) - 9 f ( x )}{x ^{10}}

What is the derivative of ({f}(x)/(x^9)) ?
The derivative of ({f}(x)/(x^9)) is (x derivative of {f}(x)-9{f}(x))/(x^{10)}
What is the first derivative of ({f}(x)/(x^9)) ?
The first derivative of ({f}(x)/(x^9)) is (x derivative of {f}(x)-9{f}(x))/(x^{10)}