What is the derivative of sqrt(7+xsec(x)) ?

The derivative of sqrt(7+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(7+xsec(x)))

What is the first derivative of sqrt(7+xsec(x)) ?

The first derivative of sqrt(7+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(7+xsec(x)))

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\frac{d}{d x} (7 + x sec (x))

\frac{x sec ( x ) tan ( x ) + sec ( x )}{2 7 + x sec ( x )}

Solution steps

\frac{d}{d x} (7 + x sec (x))

Apply the chain rule:

\frac{1}{2 7 + x sec ( x )} \frac{d}{d x} (7 + x sec (x))

= \frac{1}{2 7 + x sec ( x )} \frac{d}{d x} (7 + x sec (x))

\frac{d}{d x} (7 + x sec (x)) = x sec (x) tan (x) + sec (x)

= \frac{1}{2 7 + x sec ( x )} (x sec (x) tan (x) + sec (x))

Simplify

\frac{1}{2 7 + x sec ( x )} (x sec (x) tan (x) + sec (x)) : \frac{x sec ( x ) tan ( x ) + sec ( x )}{2 7 + x sec ( x )}

= \frac{x sec ( x ) tan ( x ) + sec ( x )}{2 7 + x sec ( x )}

\int x e^{- x} d x

\frac{d}{d x} (64 e^{4 x})

\frac{d}{d x} (ccos t + t^{2} sin (t))

x^{2} + 2 x + 11, - 4 x + 2, 0

f (x) = 8 x e^{9 x}

What is the derivative of sqrt(7+xsec(x)) ?
The derivative of sqrt(7+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(7+xsec(x)))
What is the first derivative of sqrt(7+xsec(x)) ?
The first derivative of sqrt(7+xsec(x)) is (xsec(x)tan(x)+sec(x))/(2sqrt(7+xsec(x)))