What is the derivative of ((x-7/(x+4))^{10}) ?

The derivative of ((x-7/(x+4))^{10}) is (110(x-7)^9)/((x+4)^{11)}

What is the first derivative of ((x-7/(x+4))^{10}) ?

The first derivative of ((x-7/(x+4))^{10}) is (110(x-7)^9)/((x+4)^{11)}

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\frac{d}{d x} ((\frac{x - 7}{x + 4})^{10})

\frac{110 ( x - 7 ) ^{9}}{( x + 4 ) ^{11}}

Solution steps

\frac{d}{d x} ((\frac{x - 7}{x + 4})^{10})

Apply the chain rule:

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

= 10 (\frac{x - 7}{x + 4})^{9} \frac{d}{d x} (\frac{x - 7}{x + 4})

\frac{d}{d x} (\frac{x - 7}{x + 4}) = \frac{11}{( x + 4 ) ^{2}}

= 10 (\frac{x - 7}{x + 4})^{9} \frac{11}{( x + 4 ) ^{2}}

Simplify

10 (\frac{x - 7}{x + 4})^{9} \frac{11}{( x + 4 ) ^{2}} : \frac{110 ( x - 7 ) ^{9}}{( x + 4 ) ^{11}}

= \frac{110 ( x - 7 ) ^{9}}{( x + 4 ) ^{11}}

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y^{^{'}} = x^{2} + 4

\frac{d}{d x} (\frac{x}{1 + ( 1.5574 + 6.09 x ^{2} ) ^{2}})

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What is the derivative of ((x-7/(x+4))^{10}) ?
The derivative of ((x-7/(x+4))^{10}) is (110(x-7)^9)/((x+4)^{11)}
What is the first derivative of ((x-7/(x+4))^{10}) ?
The first derivative of ((x-7/(x+4))^{10}) is (110(x-7)^9)/((x+4)^{11)}