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Popular >

derivative of 2-(x^2-2x+4/(x-2))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2) = 0

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

= 0 - \frac{x ^{2} - 4 x}{( x - 2 ) ^{2}}

Simplify

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

Popular Examples

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\int \frac{ln ( x )}{x} d x

x^2(d^2y)/(dx^2)-5xy^'+8y=4x^2

x^{2} \frac{d ^{2} y}{d x ^{2}} - 5 x y^{^{'}} + 8 y = 4 x^{2}

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\int_{0}^{1} 2 π (x + 1) (x^{2}) d x

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integral of 1/((x+5)^2(x-4))

\int \frac{1}{( x + 5 ) ^{2} ( x - 4 )} d x

Frequently Asked Questions (FAQ)

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