What is the derivative of ((x-3/(x+2))^{12}) ?

The derivative of ((x-3/(x+2))^{12}) is (60(x-3)^{11})/((x+2)^{13)}

What is the first derivative of ((x-3/(x+2))^{12}) ?

The first derivative of ((x-3/(x+2))^{12}) is (60(x-3)^{11})/((x+2)^{13)}

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\frac{d}{d x} ((\frac{x - 3}{x + 2})^{12})

\frac{60 ( x - 3 ) ^{11}}{( x + 2 ) ^{13}}

Solution steps

\frac{d}{d x} ((\frac{x - 3}{x + 2})^{12})

Apply the chain rule:

12 (\frac{x - 3}{x + 2})^{11} \frac{d}{d x} (\frac{x - 3}{x + 2})

= 12 (\frac{x - 3}{x + 2})^{11} \frac{d}{d x} (\frac{x - 3}{x + 2})

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

= 12 (\frac{x - 3}{x + 2})^{11} \frac{5}{( x + 2 ) ^{2}}

Simplify

12 (\frac{x - 3}{x + 2})^{11} \frac{5}{( x + 2 ) ^{2}} : \frac{60 ( x - 3 ) ^{11}}{( x + 2 ) ^{13}}

= \frac{60 ( x - 3 ) ^{11}}{( x + 2 ) ^{13}}

\frac{d}{d x} (\frac{1}{16} e^{2 x^{2}})

\frac{d}{d y} (y - y^{2})

y^{^{'}} = \frac{3 y - 4 x}{2 x - 3 x}

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

y = 2 x + 2, y = x^{2} + 2, x = - 1, x = 3

What is the derivative of ((x-3/(x+2))^{12}) ?
The derivative of ((x-3/(x+2))^{12}) is (60(x-3)^{11})/((x+2)^{13)}
What is the first derivative of ((x-3/(x+2))^{12}) ?
The first derivative of ((x-3/(x+2))^{12}) is (60(x-3)^{11})/((x+2)^{13)}