What is the derivative of sin(1/(x^2-5)) ?

The derivative of sin(1/(x^2-5)) is -(2xcos(1/(x^2-5)))/((x^2-5)^2)

What is the first derivative of sin(1/(x^2-5)) ?

The first derivative of sin(1/(x^2-5)) is -(2xcos(1/(x^2-5)))/((x^2-5)^2)

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\frac{d}{d x} (sin (\frac{1}{x ^{2} - 5}))

- \frac{2 x cos ( \frac{1}{x ^{2} - 5} )}{( x ^{2} - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (sin (\frac{1}{x ^{2} - 5}))

Apply the chain rule:

cos (\frac{1}{x ^{2} - 5}) \frac{d}{d x} (\frac{1}{x ^{2} - 5})

= cos (\frac{1}{x ^{2} - 5}) \frac{d}{d x} (\frac{1}{x ^{2} - 5})

\frac{d}{d x} (\frac{1}{x ^{2} - 5}) = - \frac{2 x}{( x ^{2} - 5 ) ^{2}}

= cos (\frac{1}{x ^{2} - 5}) (- \frac{2 x}{( x ^{2} - 5 ) ^{2}})

Simplify

cos (\frac{1}{x ^{2} - 5}) (- \frac{2 x}{( x ^{2} - 5 ) ^{2}}) : - \frac{2 x cos ( \frac{1}{x ^{2} - 5} )}{( x ^{2} - 5 ) ^{2}}

= - \frac{2 x cos ( \frac{1}{x ^{2} - 5} )}{( x ^{2} - 5 ) ^{2}}

What is the derivative of sin(1/(x^2-5)) ?
The derivative of sin(1/(x^2-5)) is -(2xcos(1/(x^2-5)))/((x^2-5)^2)
What is the first derivative of sin(1/(x^2-5)) ?
The first derivative of sin(1/(x^2-5)) is -(2xcos(1/(x^2-5)))/((x^2-5)^2)