What is the derivative of ({f}(x)/(x^4)) ?

The derivative of ({f}(x)/(x^4)) is (x derivative of {f}(x)-4{f}(x))/(x^5)

What is the first derivative of ({f}(x)/(x^4)) ?

The first derivative of ({f}(x)/(x^4)) is (x derivative of {f}(x)-4{f}(x))/(x^5)

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

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

Simplify

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

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

\frac{\partial}{\partial x} (2 x - 3 cos (x) + 10 y)

\frac{d}{d x} (\frac{8}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

x^{2} y^{^{''}} + 4 x y^{^{'}} + 2 y = 0

x \to 8 lim (x + 8)

x \to \infty lim (ln (2))

What is the derivative of ({f}(x)/(x^4)) ?
The derivative of ({f}(x)/(x^4)) is (x derivative of {f}(x)-4{f}(x))/(x^5)
What is the first derivative of ({f}(x)/(x^4)) ?
The first derivative of ({f}(x)/(x^4)) is (x derivative of {f}(x)-4{f}(x))/(x^5)