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Popular >

derivative of ((x-4)/x)

Solution

\frac{d}{d x} (\frac{( x - 4 )}{x})

Solution

\frac{4}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x - 4 )}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 4) = 1

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

= \frac{1 \cdot x - 1 \cdot ( x - 4 )}{x ^{2}}

Simplify

\frac{1 \cdot x - 1 \cdot ( x - 4 )}{x ^{2}} : \frac{4}{x ^{2}}

= \frac{4}{x ^{2}}

Popular Examples

(\partial)/(\partial x)(6xsin(8x^2y))

\frac{\partial}{\partial x} (6 x sin (8 x^{2} y))

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

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

derivative of (x^2+2x^5)

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

area y=x^2,y=x,y=2 area

y = x^{2}, y = x, y = 2

derivative of (1^2/(2^1))

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

Frequently Asked Questions (FAQ)

What is the derivative of ((x-4)/x) ?
The derivative of ((x-4)/x) is 4/(x^2)
What is the first derivative of ((x-4)/x) ?
The first derivative of ((x-4)/x) is 4/(x^2)