What is the derivative of 8/(xsqrt(x^2-4)) ?

The derivative of 8/(xsqrt(x^2-4)) is -(8(2x^2-4))/(x^2(x^2-4)sqrt(x^2-4))

What is the first derivative of 8/(xsqrt(x^2-4)) ?

The first derivative of 8/(xsqrt(x^2-4)) is -(8(2x^2-4))/(x^2(x^2-4)sqrt(x^2-4))

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derivative of

\frac{8}{x x ^{2} - 4}

- \frac{8 ( 2 x ^{2} - 4 )}{x ^{2} ( x ^{2} - 4 ) x ^{2} - 4}

Solution steps

\frac{d}{d x} (\frac{8}{x x ^{2} - 4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (\frac{1}{x x ^{2} - 4})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 8 \frac{d}{d x} ((x x^{2} - 4)^{- 1})

Apply the chain rule:

- \frac{1}{( x x ^{2} - 4 ) ^{2}} \frac{d}{d x} (x x^{2} - 4)

= - \frac{1}{( x x ^{2} - 4 ) ^{2}} \frac{d}{d x} (x x^{2} - 4)

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

= 8 (- \frac{1}{( x x ^{2} - 4 ) ^{2}} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4})

Simplify

8 (- \frac{1}{( x x ^{2} - 4 ) ^{2}} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4}) : - \frac{8 ( 2 x ^{2} - 4 )}{x ^{2} ( x ^{2} - 4 ) x ^{2} - 4}

= - \frac{8 ( 2 x ^{2} - 4 )}{x ^{2} ( x ^{2} - 4 ) x ^{2} - 4}

x \to \infty lim ((k)^{x})

x \to 1 lim (tan (x))

y^{^{'}} = \frac{( x ^{4} y ^{4} + 4 x ^{4} )}{y ^{3}}

y^{^{''}} - 3 y^{^{'}} - 4 y = - 8 e^{t} cos (2 t)

f (x) = e^{x} sin (x) - 3 e^{x} cos (x)

What is the derivative of 8/(xsqrt(x^2-4)) ?
The derivative of 8/(xsqrt(x^2-4)) is -(8(2x^2-4))/(x^2(x^2-4)sqrt(x^2-4))
What is the first derivative of 8/(xsqrt(x^2-4)) ?
The first derivative of 8/(xsqrt(x^2-4)) is -(8(2x^2-4))/(x^2(x^2-4)sqrt(x^2-4))