What is the derivative of (9-x/9)^{-7} ?

The derivative of (9-x/9)^{-7} is (33480783)/((81-x)^8)

What is the first derivative of (9-x/9)^{-7} ?

The first derivative of (9-x/9)^{-7} is (33480783)/((81-x)^8)

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derivative of

(9 - \frac{x}{9})^{- 7}

\frac{33480783}{( 81 - x ) ^{8}}

Solution steps

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

Apply the chain rule:

- \frac{7}{( 9 - \frac{x}{9} ) ^{8}} \frac{d}{d x} (9 - \frac{x}{9})

= - \frac{7}{( 9 - \frac{x}{9} ) ^{8}} \frac{d}{d x} (9 - \frac{x}{9})

\frac{d}{d x} (9 - \frac{x}{9}) = - \frac{1}{9}

= - \frac{7}{( 9 - \frac{x}{9} ) ^{8}} (- \frac{1}{9})

Simplify

- \frac{7}{( 9 - \frac{x}{9} ) ^{8}} (- \frac{1}{9}) : \frac{33480783}{( 81 - x ) ^{8}}

= \frac{33480783}{( 81 - x ) ^{8}}

x = - 2, x = 1, y = 7 x, y = x^{2} - 8

\frac{d y}{d x}, 6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0

2 x + 1

y^{^{''}} - 3 y^{^{'}} + 18 y = 0

What is the derivative of (9-x/9)^{-7} ?
The derivative of (9-x/9)^{-7} is (33480783)/((81-x)^8)
What is the first derivative of (9-x/9)^{-7} ?
The first derivative of (9-x/9)^{-7} is (33480783)/((81-x)^8)