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

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

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

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

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\frac{d}{d 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}}

(6 - 2 x^{2})^{3}

n = 0 \sum \infty n (\frac{3}{5})^{n}

25 x^{2} y^{^{''}} + 25 x y^{^{'}} + y = 0

x \to \infty lim (x^{x})

\int_{7}^{12} ln (x^{3}) d x

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