What is the derivative of xtan(1/x) ?

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

What is the first derivative of xtan(1/x) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = tan (\frac{1}{x})

= \frac{d x}{d x} tan (\frac{1}{x}) + \frac{d}{d x} (tan (\frac{1}{x})) x

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int \frac{1}{( x + 3 ) ^{2} ( x - 5 )} d x

cos^{3} (12 x)

y = 3 x^{2} + 2 x, (2, 4)

\int sin^{2} (x co) s^{2} x d x

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