What is the derivative of (x^2-3x+11)/(x^2+x-3) ?

The derivative of (x^2-3x+11)/(x^2+x-3) is (4x^2-28x-2)/((x^2+x-3)^2)

What is the first derivative of (x^2-3x+11)/(x^2+x-3) ?

The first derivative of (x^2-3x+11)/(x^2+x-3) is (4x^2-28x-2)/((x^2+x-3)^2)

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derivative of

\frac{x ^{2} - 3 x + 11}{x ^{2} + x - 3}

\frac{4 x ^{2} - 28 x - 2}{( x ^{2} + x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 3 x + 11}{x ^{2} + 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} - 3 x + 11 ) ( x ^{2} + x - 3 ) - \frac{d}{d x} ( x ^{2} + x - 3 ) ( x ^{2} - 3 x + 11 )}{( x ^{2} + x - 3 ) ^{2}}

\frac{d}{d x} (x^{2} - 3 x + 11) = 2 x - 3

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

= \frac{( 2 x - 3 ) ( x ^{2} + x - 3 ) - ( 2 x + 1 ) ( x ^{2} - 3 x + 11 )}{( x ^{2} + x - 3 ) ^{2}}

Expand

(2 x - 3) (x^{2} + x - 3) - (2 x + 1) (x^{2} - 3 x + 11) : 4 x^{2} - 28 x - 2

= \frac{4 x ^{2} - 28 x - 2}{( x ^{2} + x - 3 ) ^{2}}

\frac{\partial}{\partial θ} (cos (θ))

x \to 0 lim (\frac{x}{2})

f (x) = e^{x + 1}

x^{\frac{1}{3}} + \frac{x - 4}{3 x ^{\frac{5}{3}}}

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

What is the derivative of (x^2-3x+11)/(x^2+x-3) ?
The derivative of (x^2-3x+11)/(x^2+x-3) is (4x^2-28x-2)/((x^2+x-3)^2)
What is the first derivative of (x^2-3x+11)/(x^2+x-3) ?
The first derivative of (x^2-3x+11)/(x^2+x-3) is (4x^2-28x-2)/((x^2+x-3)^2)