What is the derivative of y=(f(x))/(x^4) ?

The derivative of y=(f(x))/(x^4) is (x\frac{df)/(dx)-4f(x)}{x^5}

What is the first derivative of y=(f(x))/(x^4) ?

The first derivative of y=(f(x))/(x^4) is (x\frac{df)/(dx)-4f(x)}{x^5}

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derivative of

y = \frac{f ( x )}{x ^{4}}

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

Solution steps

\frac{d}{d x} (\frac{f ( x )}{x ^{4}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{\frac{df}{d x} x ^{4} - 4 x ^{3} f ( x )}{( x ^{4} ) ^{2}}

Simplify

\frac{\frac{df}{d x} x ^{4} - 4 x ^{3} f ( x )}{( x ^{4} ) ^{2}} : \frac{x \frac{df}{d x} - 4 f ( x )}{x ^{5}}

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

\frac{d}{d x} (e^{x^{2}} - cos (x))

\int \frac{4}{x ^{5}} d x

\frac{d}{d x} (\frac{4 x + 6}{x + 3})

\frac{d}{d x} (3^{x} ln (x))

- 3 e^{- t}

What is the derivative of y=(f(x))/(x^4) ?
The derivative of y=(f(x))/(x^4) is (x\frac{df)/(dx)-4f(x)}{x^5}
What is the first derivative of y=(f(x))/(x^4) ?
The first derivative of y=(f(x))/(x^4) is (x\frac{df)/(dx)-4f(x)}{x^5}