What is the derivative of ((x-9/(x+2))^{3/2}) ?

The derivative of ((x-9/(x+2))^{3/2}) is (33(x-9)^{1/2})/(2(x+2)^{5/2)}

What is the first derivative of ((x-9/(x+2))^{3/2}) ?

The first derivative of ((x-9/(x+2))^{3/2}) is (33(x-9)^{1/2})/(2(x+2)^{5/2)}

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\frac{d}{d x} ((\frac{x - 9}{x + 2})^{\frac{3}{2}})

\frac{33 ( x - 9 ) ^{\frac{1}{2}}}{2 ( x + 2 ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} ((\frac{x - 9}{x + 2})^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( \frac{x - 9}{x + 2} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x - 9}{x + 2})

= \frac{3 ( \frac{x - 9}{x + 2} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x - 9}{x + 2})

\frac{d}{d x} (\frac{x - 9}{x + 2}) = \frac{11}{( x + 2 ) ^{2}}

= \frac{3 ( \frac{x - 9}{x + 2} ) ^{\frac{1}{2}}}{2} \cdot \frac{11}{( x + 2 ) ^{2}}

Simplify

\frac{3 ( \frac{x - 9}{x + 2} ) ^{\frac{1}{2}}}{2} \cdot \frac{11}{( x + 2 ) ^{2}} : \frac{33 ( x - 9 ) ^{\frac{1}{2}}}{2 ( x + 2 ) ^{\frac{5}{2}}}

= \frac{33 ( x - 9 ) ^{\frac{1}{2}}}{2 ( x + 2 ) ^{\frac{5}{2}}}

What is the derivative of ((x-9/(x+2))^{3/2}) ?
The derivative of ((x-9/(x+2))^{3/2}) is (33(x-9)^{1/2})/(2(x+2)^{5/2)}
What is the first derivative of ((x-9/(x+2))^{3/2}) ?
The first derivative of ((x-9/(x+2))^{3/2}) is (33(x-9)^{1/2})/(2(x+2)^{5/2)}