What is the derivative of ((x^2+3)/(x^2-3))^8 ?

The derivative of ((x^2+3)/(x^2-3))^8 is -(96x(x^2+3)^7)/((x^2-3)^9)

What is the first derivative of ((x^2+3)/(x^2-3))^8 ?

The first derivative of ((x^2+3)/(x^2-3))^8 is -(96x(x^2+3)^7)/((x^2-3)^9)

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derivative of

(\frac{x ^{2} + 3}{x ^{2} - 3})^{8}

- \frac{96 x ( x ^{2} + 3 ) ^{7}}{( x ^{2} - 3 ) ^{9}}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 3}{x ^{2} - 3})^{8})

Apply the chain rule:

8 (\frac{x ^{2} + 3}{x ^{2} - 3})^{7} \frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

= 8 (\frac{x ^{2} + 3}{x ^{2} - 3})^{7} \frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

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

= 8 (\frac{x ^{2} + 3}{x ^{2} - 3})^{7} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

Simplify

8 (\frac{x ^{2} + 3}{x ^{2} - 3})^{7} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{96 x ( x ^{2} + 3 ) ^{7}}{( x ^{2} - 3 ) ^{9}}

= - \frac{96 x ( x ^{2} + 3 ) ^{7}}{( x ^{2} - 3 ) ^{9}}

\frac{d y}{d x} = 0.2 (4000 - y)

\frac{\partial}{\partial x} (\frac{x y}{1 + x ^{2} + y ^{2}})

\frac{d}{d x} (cos^{2} (2 x) - x^{2})

\frac{\partial}{\partial x} (cos (3 x + 4 y))

What is the derivative of ((x^2+3)/(x^2-3))^8 ?
The derivative of ((x^2+3)/(x^2-3))^8 is -(96x(x^2+3)^7)/((x^2-3)^9)
What is the first derivative of ((x^2+3)/(x^2-3))^8 ?
The first derivative of ((x^2+3)/(x^2-3))^8 is -(96x(x^2+3)^7)/((x^2-3)^9)