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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Simplify

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

Popular Examples

tangent of f(x)=6x^2+2x-7,\at x=-4 tangent of

f (x) = 6 x^{2} + 2 x - 7, at x = - 4

derivative of (1+e^{x^2})^3 derivative of

(1 + e^{x^{2}})^{3}

(\partial)/(\partial z)(x+y/z)

\frac{\partial}{\partial z} (x + \frac{y}{z})

sum from n=0 to infinity of 1/(n+4)

n = 0 \sum \infty \frac{1}{n + 4}

integral of x(x^2+1)^{10}

\int x (x^{2} + 1)^{10} d x

Frequently Asked Questions (FAQ)

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