What is the derivative of ((x-7/(x-9))^4) ?

The derivative of ((x-7/(x-9))^4) is -(8(x-7)^3)/((x-9)^5)

What is the first derivative of ((x-7/(x-9))^4) ?

The first derivative of ((x-7/(x-9))^4) is -(8(x-7)^3)/((x-9)^5)

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\frac{d}{d x} ((\frac{x - 7}{x - 9})^{4})

- \frac{8 ( x - 7 ) ^{3}}{( x - 9 ) ^{5}}

Solution steps

\frac{d}{d x} ((\frac{x - 7}{x - 9})^{4})

Apply the chain rule:

4 (\frac{x - 7}{x - 9})^{3} \frac{d}{d x} (\frac{x - 7}{x - 9})

= 4 (\frac{x - 7}{x - 9})^{3} \frac{d}{d x} (\frac{x - 7}{x - 9})

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

= 4 (\frac{x - 7}{x - 9})^{3} (- \frac{2}{( x - 9 ) ^{2}})

Simplify

4 (\frac{x - 7}{x - 9})^{3} (- \frac{2}{( x - 9 ) ^{2}}) : - \frac{8 ( x - 7 ) ^{3}}{( x - 9 ) ^{5}}

= - \frac{8 ( x - 7 ) ^{3}}{( x - 9 ) ^{5}}

\int \frac{ln ( 20 x )}{x} d x

\frac{d}{d y} (- e^{y})

\frac{d ^{2} y}{d x ^{2}} + 16 y = 0

f (x) = - x^{3} + 2 x - e^{- x} - 3

\frac{3}{\frac{s + 2}{s}}

What is the derivative of ((x-7/(x-9))^4) ?
The derivative of ((x-7/(x-9))^4) is -(8(x-7)^3)/((x-9)^5)
What is the first derivative of ((x-7/(x-9))^4) ?
The first derivative of ((x-7/(x-9))^4) is -(8(x-7)^3)/((x-9)^5)