What is the derivative of y=(f(x))/(x^9) ?

The derivative of y=(f(x))/(x^9) is (x\frac{df)/(dx)-9f(x)}{x^{10}}

What is the first derivative of y=(f(x))/(x^9) ?

The first derivative of y=(f(x))/(x^9) is (x\frac{df)/(dx)-9f(x)}{x^{10}}

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derivative of

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

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

Simplify

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

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

sin (x) cos (x) - sin^{2} (x) + x

f (x) = \frac{x}{5}, at x = 125

\int 3 x e^{- x} d x

\int (y + 1)^{2} d y

x \to 0 lim (\frac{e ^{8 x} - 1}{x})

What is the derivative of y=(f(x))/(x^9) ?
The derivative of y=(f(x))/(x^9) is (x\frac{df)/(dx)-9f(x)}{x^{10}}
What is the first derivative of y=(f(x))/(x^9) ?
The first derivative of y=(f(x))/(x^9) is (x\frac{df)/(dx)-9f(x)}{x^{10}}