What is the derivative of y=(f(x))/(x^5) ?

The derivative of y=(f(x))/(x^5) is (x\frac{df)/(dx)-5f(x)}{x^6}

What is the first derivative of y=(f(x))/(x^5) ?

The first derivative of y=(f(x))/(x^5) is (x\frac{df)/(dx)-5f(x)}{x^6}

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derivative of

y = \frac{f ( x )}{x ^{5}}

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

Simplify

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

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

2 tan^{2} (7 x)

(2 x y + 3) d x + (x^{2} - 1) d y = 0

3 x y^{^{'}} + 7 y = 0

\frac{e ^{10 x} + e ^{- 10 x}}{x}

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

What is the derivative of y=(f(x))/(x^5) ?
The derivative of y=(f(x))/(x^5) is (x\frac{df)/(dx)-5f(x)}{x^6}
What is the first derivative of y=(f(x))/(x^5) ?
The first derivative of y=(f(x))/(x^5) is (x\frac{df)/(dx)-5f(x)}{x^6}