What is the derivative of sqrt(x)sec(x+3) ?

The derivative of sqrt(x)sec(x+3) is sqrt(x)sec(x)tan(x)+(sec(x))/(2sqrt(x))

What is the first derivative of sqrt(x)sec(x+3) ?

The first derivative of sqrt(x)sec(x+3) is sqrt(x)sec(x)tan(x)+(sec(x))/(2sqrt(x))

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\frac{d}{d x} (x sec (x) + 3)

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

Solution steps

\frac{d}{d x} (x sec (x) + 3)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x sec (x)) + \frac{d}{d x} (3)

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

\frac{d}{d x} (3) = 0

= \frac{sec ( x )}{2 x} + x sec (x) tan (x) + 0

Simplify

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

What is the derivative of sqrt(x)sec(x+3) ?
The derivative of sqrt(x)sec(x+3) is sqrt(x)sec(x)tan(x)+(sec(x))/(2sqrt(x))
What is the first derivative of sqrt(x)sec(x+3) ?
The first derivative of sqrt(x)sec(x+3) is sqrt(x)sec(x)tan(x)+(sec(x))/(2sqrt(x))