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Popular >

derivative of y=((x^9))/(f(x))

Solution

derivative of

y = \frac{( x ^{9} )}{f ( x )}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of y=((x^9))/(f(x)) ?
The derivative of y=((x^9))/(f(x)) is (9x^8f(x)-\frac{df)/(dx)x^9}{f(x)^2}
What is the first derivative of y=((x^9))/(f(x)) ?
The first derivative of y=((x^9))/(f(x)) is (9x^8f(x)-\frac{df)/(dx)x^9}{f(x)^2}