What is the derivative of f(x)=(7x^2-x+9)/(6-7x) ?

The derivative of f(x)=(7x^2-x+9)/(6-7x) is (-49x^2+84x+57)/((6-7x)^2)

What is the first derivative of f(x)=(7x^2-x+9)/(6-7x) ?

The first derivative of f(x)=(7x^2-x+9)/(6-7x) is (-49x^2+84x+57)/((6-7x)^2)

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derivative of

f (x) = \frac{7 x ^{2} - x + 9}{6 - 7 x}

\frac{- 49 x ^{2} + 84 x + 57}{( 6 - 7 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x ^{2} - x + 9}{6 - 7 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 x ^{2} - x + 9 ) ( 6 - 7 x ) - \frac{d}{d x} ( 6 - 7 x ) ( 7 x ^{2} - x + 9 )}{( 6 - 7 x ) ^{2}}

\frac{d}{d x} (7 x^{2} - x + 9) = 14 x - 1

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

= \frac{( 14 x - 1 ) ( 6 - 7 x ) - ( - 7 ) ( 7 x ^{2} - x + 9 )}{( 6 - 7 x ) ^{2}}

Simplify

\frac{( 14 x - 1 ) ( 6 - 7 x ) - ( - 7 ) ( 7 x ^{2} - x + 9 )}{( 6 - 7 x ) ^{2}} : \frac{- 49 x ^{2} + 84 x + 57}{( 6 - 7 x ) ^{2}}

= \frac{- 49 x ^{2} + 84 x + 57}{( 6 - 7 x ) ^{2}}

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

2 (3 x^{2} ln (10 x) + x^{2})

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\frac{d}{d x} (\frac{1}{3} x x^{2} + 5)

What is the derivative of f(x)=(7x^2-x+9)/(6-7x) ?
The derivative of f(x)=(7x^2-x+9)/(6-7x) is (-49x^2+84x+57)/((6-7x)^2)
What is the first derivative of f(x)=(7x^2-x+9)/(6-7x) ?
The first derivative of f(x)=(7x^2-x+9)/(6-7x) is (-49x^2+84x+57)/((6-7x)^2)