What is the derivative of ({f}(x)/(x^5)) ?

The derivative of ({f}(x)/(x^5)) is (x derivative of {f}(x)-5{f}(x))/(x^6)

What is the first derivative of ({f}(x)/(x^5)) ?

The first derivative of ({f}(x)/(x^5)) is (x derivative of {f}(x)-5{f}(x))/(x^6)

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\frac{d}{d x} (\frac{f ( x )}{x ^{5}})

\frac{x \frac{d}{d x} ( f ( x ) ) - 5 f ( x )}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{f ( x )}{x ^{5}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( f ( x ) ) x ^{5} - \frac{d}{d x} ( x ^{5} ) f ( x )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{\frac{d}{d x} ( f ( x ) ) x ^{5} - 5 x ^{4} f ( x )}{( x ^{5} ) ^{2}}

Simplify

\frac{\frac{d}{d x} ( f ( x ) ) x ^{5} - 5 x ^{4} f ( x )}{( x ^{5} ) ^{2}} : \frac{x \frac{d}{d x} ( f ( x ) ) - 5 f ( x )}{x ^{6}}

= \frac{x \frac{d}{d x} ( f ( x ) ) - 5 f ( x )}{x ^{6}}

(5 x + 2)^{4} (2 x - 3)^{8}

3 \cdot \frac{d y}{d x} + 12 y = 4

\frac{\partial}{\partial x} (x^{3} z)

x \to 1.2 lim (\frac{1}{x - 2})

\int \frac{( x ^{2} - x + 6 )}{x ^{3} + 3 x} d x

What is the derivative of ({f}(x)/(x^5)) ?
The derivative of ({f}(x)/(x^5)) is (x derivative of {f}(x)-5{f}(x))/(x^6)
What is the first derivative of ({f}(x)/(x^5)) ?
The first derivative of ({f}(x)/(x^5)) is (x derivative of {f}(x)-5{f}(x))/(x^6)