What is the solution for -derivative of f(x)=arcsec(x) ?

The solution for -derivative of f(x)=arcsec(x) is f(x)=-xarcsec(x)+ln(x+sqrt(x^2-1))+c_{1}

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Find the Derivative - d/dx f(x)=arcsec(x)

- \frac{d}{d x} f (x) = arcsec (x)

f (x) = - x arcsec (x) + ln (x + x^{2} - 1) + c_{1}

Solution steps

- \frac{df}{d x} = arcsec (x)

Isolate

f^{'} (x) : f^{'} (x) = - arcsec (x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int - arcsec (x) d x

\int - arcsec (x) d x = - x arcsec (x) + ln (x + x^{2} - 1) + c_{1}

f (x) = - x arcsec (x) + ln (x + x^{2} - 1) + c_{1}

- \frac{d}{d x} (\frac{x}{4})

- \frac{d}{d x} (\frac{100}{x})

- \frac{d}{d x} (2 x y)

f (x) = x^{2} + 2 x, 0 < x < 6

- \frac{d}{d x} (tan (3 x))

What is the solution for -derivative of f(x)=arcsec(x) ?
The solution for -derivative of f(x)=arcsec(x) is f(x)=-xarcsec(x)+ln(x+sqrt(x^2-1))+c_{1}