What is the derivative of x^4sec(5/x) ?

The derivative of x^4sec(5/x) is 4x^3sec(5/x)-5x^2sec(5/x)tan(5/x)

What is the first derivative of x^4sec(5/x) ?

The first derivative of x^4sec(5/x) is 4x^3sec(5/x)-5x^2sec(5/x)tan(5/x)

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derivative of

x^{4} sec (\frac{5}{x})

4 x^{3} sec (\frac{5}{x}) - 5 x^{2} sec (\frac{5}{x}) tan (\frac{5}{x})

Solution steps

\frac{d}{d x} (x^{4} sec (\frac{5}{x}))

Apply the Product Rule:

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

f = x^{4}, g = sec (\frac{5}{x})

= \frac{d}{d x} (x^{4}) sec (\frac{5}{x}) + \frac{d}{d x} (sec (\frac{5}{x})) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} sec (\frac{5}{x}) + (- \frac{5 sec ( \frac{5}{x} ) tan ( \frac{5}{x} )}{x ^{2}}) x^{4}

Simplify

4 x^{3} sec (\frac{5}{x}) + (- \frac{5 sec ( \frac{5}{x} ) tan ( \frac{5}{x} )}{x ^{2}}) x^{4} : 4 x^{3} sec (\frac{5}{x}) - 5 x^{2} sec (\frac{5}{x}) tan (\frac{5}{x})

= 4 x^{3} sec (\frac{5}{x}) - 5 x^{2} sec (\frac{5}{x}) tan (\frac{5}{x})

What is the derivative of x^4sec(5/x) ?
The derivative of x^4sec(5/x) is 4x^3sec(5/x)-5x^2sec(5/x)tan(5/x)
What is the first derivative of x^4sec(5/x) ?
The first derivative of x^4sec(5/x) is 4x^3sec(5/x)-5x^2sec(5/x)tan(5/x)