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Popular Calculus >

derivative of x/({f(x)})

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

= \frac{1 \cdot f ( x ) - \frac{d}{d x} ( f ( x ) ) x}{f ( x ) ^{2}}

Simplify

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

Popular Examples

2yy^'-xy^'=y-2x

2 y y^{^{'}} - x y^{^{'}} = y - 2 x

integral of (2ysin(x)-x^3+ln(y))

\int (2 y sin (x) - x^{3} + ln (y)) d y

y^{''}-9y^'=81t

y^{^{''}} - 9 y^{^{'}} = 81 t

derivative of (arccos(x)/x)

\frac{d}{d x} (\frac{arccos ( x )}{x})

derivative of tan(x+1/(x^2))

\frac{d}{d x} (tan (x) + \frac{1}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of x/({f(x)}) ?
The derivative of x/({f(x)}) is ({f}(x)-x derivative of {f}(x))/({f)(x)^2}
What is the first derivative of x/({f(x)}) ?
The first derivative of x/({f(x)}) is ({f}(x)-x derivative of {f}(x))/({f)(x)^2}