derivative x^2*sec(1/x)

解答

导数

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

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

求解步骤

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

使用微分乘法定则:

(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}

化简

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

in v erse l a pl a ce \frac{s + 2}{s ^{2} + 4}

t an g e n t f (x) = \frac{3 x}{x - 2}, (4, 6)

d er i v a t i v e \frac{4}{r ^{3}}

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