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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Simplify

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

Popular Examples

integral from 0 to 2 of (y-2)^2

\int_{0}^{2} (y - 2)^{2} d y

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

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

integral of 1/((x+6)^2)

\int \frac{1}{( x + 6 ) ^{2}} d x

derivative of (2x^2-5x+7^3)

\frac{d}{d x} ((2 x^{2} - 5 x + 7)^{3})

integral of θsin(θ)

\int θ sin (θ) d θ

Frequently Asked Questions (FAQ)

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