What is the derivative of x^2*sec(1/x) ?

The derivative of x^2*sec(1/x) is 2xsec(1/x)-sec(1/x)tan(1/x)

What is the first derivative of x^2*sec(1/x) ?

The first derivative of x^2*sec(1/x) is 2xsec(1/x)-sec(1/x)tan(1/x)

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derivative of

x^{2} \cdot sec (\frac{1}{x})

2 x sec (\frac{1}{x}) - sec (\frac{1}{x}) tan (\frac{1}{x})

Solution steps

\frac{d}{d x} (x^{2} sec (\frac{1}{x}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = sec (\frac{1}{x})

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

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

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

= 2 x sec (\frac{1}{x}) + (- \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} )}{x ^{2}}) x^{2}

Simplify

2 x sec (\frac{1}{x}) + (- \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} )}{x ^{2}}) x^{2} : 2 x sec (\frac{1}{x}) - sec (\frac{1}{x}) tan (\frac{1}{x})

= 2 x sec (\frac{1}{x}) - sec (\frac{1}{x}) tan (\frac{1}{x})

\int_{1}^{3} (4 x^{3} + 2) d x

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

\frac{s + 2}{s ^{2} + 4}

f (x) = \frac{3 x}{x - 2}, (4, 6)

\frac{4}{r ^{3}}

What is the derivative of x^2*sec(1/x) ?
The derivative of x^2*sec(1/x) is 2xsec(1/x)-sec(1/x)tan(1/x)
What is the first derivative of x^2*sec(1/x) ?
The first derivative of x^2*sec(1/x) is 2xsec(1/x)-sec(1/x)tan(1/x)