What is the derivative of (x^2-3x+2/(x^7-2)) ?

The derivative of (x^2-3x+2/(x^7-2)) is (-5x^8+18x^7-14x^6-4x+6)/((x^7-2)^2)

What is the first derivative of (x^2-3x+2/(x^7-2)) ?

The first derivative of (x^2-3x+2/(x^7-2)) is (-5x^8+18x^7-14x^6-4x+6)/((x^7-2)^2)

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\frac{d}{d x} (\frac{x ^{2} - 3 x + 2}{x ^{7} - 2})

\frac{- 5 x ^{8} + 18 x ^{7} - 14 x ^{6} - 4 x + 6}{( x ^{7} - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 3 x + 2}{x ^{7} - 2})

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 + 2 ) ( x ^{7} - 2 ) - \frac{d}{d x} ( x ^{7} - 2 ) ( x ^{2} - 3 x + 2 )}{( x ^{7} - 2 ) ^{2}}

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

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

= \frac{( 2 x - 3 ) ( x ^{7} - 2 ) - 7 x ^{6} ( x ^{2} - 3 x + 2 )}{( x ^{7} - 2 ) ^{2}}

Expand

(2 x - 3) (x^{7} - 2) - 7 x^{6} (x^{2} - 3 x + 2) : - 5 x^{8} + 18 x^{7} - 14 x^{6} - 4 x + 6

= \frac{- 5 x ^{8} + 18 x ^{7} - 14 x ^{6} - 4 x + 6}{( x ^{7} - 2 ) ^{2}}

\frac{d y}{d x} + \frac{2 x}{1 + x ^{2}} y = \frac{1}{1 + x ^{2}}

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

\frac{d}{d x} (\frac{1}{2 sin ( x )})

2 sin (x)

\frac{\partial}{\partial m} (- m g (m) sin (a))

What is the derivative of (x^2-3x+2/(x^7-2)) ?
The derivative of (x^2-3x+2/(x^7-2)) is (-5x^8+18x^7-14x^6-4x+6)/((x^7-2)^2)
What is the first derivative of (x^2-3x+2/(x^7-2)) ?
The first derivative of (x^2-3x+2/(x^7-2)) is (-5x^8+18x^7-14x^6-4x+6)/((x^7-2)^2)