What is the derivative of y=(f(x))/(x^6) ?

The derivative of y=(f(x))/(x^6) is (x\frac{df)/(dx)-6f(x)}{x^7}

What is the first derivative of y=(f(x))/(x^6) ?

The first derivative of y=(f(x))/(x^6) is (x\frac{df)/(dx)-6f(x)}{x^7}

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derivative of

y = \frac{f ( x )}{x ^{6}}

\frac{x \frac{df}{d x} - 6 f ( x )}{x ^{7}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{df}{d x} x ^{6} - \frac{d}{d x} ( x ^{6} ) f ( x )}{( x ^{6} ) ^{2}}

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

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

Simplify

\frac{\frac{df}{d x} x ^{6} - 6 x ^{5} f ( x )}{( x ^{6} ) ^{2}} : \frac{x \frac{df}{d x} - 6 f ( x )}{x ^{7}}

= \frac{x \frac{df}{d x} - 6 f ( x )}{x ^{7}}

What is the derivative of y=(f(x))/(x^6) ?
The derivative of y=(f(x))/(x^6) is (x\frac{df)/(dx)-6f(x)}{x^7}
What is the first derivative of y=(f(x))/(x^6) ?
The first derivative of y=(f(x))/(x^6) is (x\frac{df)/(dx)-6f(x)}{x^7}