What is the derivative of cos(pi/2+1/x) ?

The derivative of cos(pi/2+1/x) is (cos(1/x))/(x^2)

What is the first derivative of cos(pi/2+1/x) ?

The first derivative of cos(pi/2+1/x) is (cos(1/x))/(x^2)

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\frac{d}{d x} (cos (\frac{π}{2} + \frac{1}{x}))

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

Solution steps

\frac{d}{d x} (cos (\frac{π}{2} + \frac{1}{x}))

Simplify

cos (\frac{π}{2} + \frac{1}{x}) : - sin (\frac{1}{x})

= \frac{d}{d x} (- sin (\frac{1}{x}))

Take the constant out:

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

= - \frac{d}{d x} (sin (\frac{1}{x}))

Apply the chain rule:

cos (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

= cos (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

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

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

Simplify

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

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

What is the derivative of cos(pi/2+1/x) ?
The derivative of cos(pi/2+1/x) is (cos(1/x))/(x^2)
What is the first derivative of cos(pi/2+1/x) ?
The first derivative of cos(pi/2+1/x) is (cos(1/x))/(x^2)