What is the derivative of f(x)=(x^2+5)/(x-2) ?

The derivative of f(x)=(x^2+5)/(x-2) is (x^2-4x-5)/((x-2)^2)

What is the first derivative of f(x)=(x^2+5)/(x-2) ?

The first derivative of f(x)=(x^2+5)/(x-2) is (x^2-4x-5)/((x-2)^2)

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derivative of

f (x) = \frac{x ^{2} + 5}{x - 2}

\frac{x ^{2} - 4 x - 5}{( x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{2 x ( x - 2 ) - 1 \cdot ( x ^{2} + 5 )}{( x - 2 ) ^{2}}

Simplify

\frac{2 x ( x - 2 ) - 1 \cdot ( x ^{2} + 5 )}{( x - 2 ) ^{2}} : \frac{x ^{2} - 4 x - 5}{( x - 2 ) ^{2}}

= \frac{x ^{2} - 4 x - 5}{( x - 2 ) ^{2}}

What is the derivative of f(x)=(x^2+5)/(x-2) ?
The derivative of f(x)=(x^2+5)/(x-2) is (x^2-4x-5)/((x-2)^2)
What is the first derivative of f(x)=(x^2+5)/(x-2) ?
The first derivative of f(x)=(x^2+5)/(x-2) is (x^2-4x-5)/((x-2)^2)