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Popular >

derivative of (x-3)/x

Solution

derivative of

\frac{x - 3}{x}

Solution

\frac{3}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 3}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 3) = 1

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

= \frac{1 \cdot x - 1 \cdot ( x - 3 )}{x ^{2}}

Simplify

\frac{1 \cdot x - 1 \cdot ( x - 3 )}{x ^{2}} : \frac{3}{x ^{2}}

= \frac{3}{x ^{2}}

Popular Examples

integral of 1/(x^2+4x+2)

\int \frac{1}{x ^{2} + 4 x + 2} d x

x^3y^'+2x^2y=4cos(4x)y^{-1/2}

x^{3} y^{^{'}} + 2 x^{2} y = 4 cos (4 x) y^{- \frac{1}{2}}

derivative of f(x)=sqrt(log_{a)(x)}derivative of

f (x) = lo g_{a} (x)

(\partial)/(\partial x)(x^{1/2}+y)

\frac{\partial}{\partial x} (x^{\frac{1}{2}} + y)

tangent of y=4e^x tangent of

y = 4 e^{x}

Frequently Asked Questions (FAQ)

What is the derivative of (x-3)/x ?
The derivative of (x-3)/x is 3/(x^2)
What is the first derivative of (x-3)/x ?
The first derivative of (x-3)/x is 3/(x^2)