What is the derivative of (x^2+1/(x-3)) ?

The derivative of (x^2+1/(x-3)) is (x^2-6x-1)/((x-3)^2)

What is the first derivative of (x^2+1/(x-3)) ?

The first derivative of (x^2+1/(x-3)) is (x^2-6x-1)/((x-3)^2)

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\frac{d}{d x} (\frac{x ^{2} + 1}{x - 3})

\frac{x ^{2} - 6 x - 1}{( x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 1}{x - 3})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( x - 3 ) - 1 \cdot ( x ^{2} + 1 )}{( x - 3 ) ^{2}} : \frac{x ^{2} - 6 x - 1}{( x - 3 ) ^{2}}

= \frac{x ^{2} - 6 x - 1}{( x - 3 ) ^{2}}

x \to - 8 lim (- \frac{3}{7} x + \frac{10}{11})

\frac{d}{d x} (\frac{7}{x - 1})

f (x) = x^{2}, (2, 4)

\int x + \frac{1}{x} d x

What is the derivative of (x^2+1/(x-3)) ?
The derivative of (x^2+1/(x-3)) is (x^2-6x-1)/((x-3)^2)
What is the first derivative of (x^2+1/(x-3)) ?
The first derivative of (x^2+1/(x-3)) is (x^2-6x-1)/((x-3)^2)