What is the derivative of (x^2-7x+6/(x^2+7)) ?

The derivative of (x^2-7x+6/(x^2+7)) is (7x^2+2x-49)/((x^2+7)^2)

What is the first derivative of (x^2-7x+6/(x^2+7)) ?

The first derivative of (x^2-7x+6/(x^2+7)) is (7x^2+2x-49)/((x^2+7)^2)

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\frac{d}{d x} (\frac{x ^{2} - 7 x + 6}{x ^{2} + 7})

\frac{7 x ^{2} + 2 x - 49}{( x ^{2} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 7 x + 6}{x ^{2} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 7 x + 6 ) ( x ^{2} + 7 ) - \frac{d}{d x} ( x ^{2} + 7 ) ( x ^{2} - 7 x + 6 )}{( x ^{2} + 7 ) ^{2}}

\frac{d}{d x} (x^{2} - 7 x + 6) = 2 x - 7

\frac{d}{d x} (x^{2} + 7) = 2 x

= \frac{( 2 x - 7 ) ( x ^{2} + 7 ) - 2 x ( x ^{2} - 7 x + 6 )}{( x ^{2} + 7 ) ^{2}}

Expand

(2 x - 7) (x^{2} + 7) - 2 x (x^{2} - 7 x + 6) : 7 x^{2} + 2 x - 49

= \frac{7 x ^{2} + 2 x - 49}{( x ^{2} + 7 ) ^{2}}

What is the derivative of (x^2-7x+6/(x^2+7)) ?
The derivative of (x^2-7x+6/(x^2+7)) is (7x^2+2x-49)/((x^2+7)^2)
What is the first derivative of (x^2-7x+6/(x^2+7)) ?
The first derivative of (x^2-7x+6/(x^2+7)) is (7x^2+2x-49)/((x^2+7)^2)