What is the derivative of sqrt(5+xsec(x)) ?

The derivative of sqrt(5+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(5+xsec(x)))

What is the first derivative of sqrt(5+xsec(x)) ?

The first derivative of sqrt(5+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(5+xsec(x)))

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\frac{d}{d x} (5 + x sec (x))

\frac{x sec ( x ) tan ( x ) + sec ( x )}{2 5 + x sec ( x )}

Solution steps

\frac{d}{d x} (5 + x sec (x))

Apply the chain rule:

\frac{1}{2 5 + x sec ( x )} \frac{d}{d x} (5 + x sec (x))

= \frac{1}{2 5 + x sec ( x )} \frac{d}{d x} (5 + x sec (x))

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

= \frac{1}{2 5 + x sec ( x )} (x sec (x) tan (x) + sec (x))

Simplify

\frac{1}{2 5 + x sec ( x )} (x sec (x) tan (x) + sec (x)) : \frac{x sec ( x ) tan ( x ) + sec ( x )}{2 5 + x sec ( x )}

= \frac{x sec ( x ) tan ( x ) + sec ( x )}{2 5 + x sec ( x )}

x \to 2 lim (5 x - 3)

\frac{1}{x - 2}

\frac{d}{d x} (e^{n x})

\frac{d y}{d x} = e^{4 x - 3 y}

2 x^{2} - 7 x + 5, at x = 2

What is the derivative of sqrt(5+xsec(x)) ?
The derivative of sqrt(5+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(5+xsec(x)))
What is the first derivative of sqrt(5+xsec(x)) ?
The first derivative of sqrt(5+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(5+xsec(x)))