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Popular Calculus >

derivative of e^2+(sec(x)sqrt(x))

Solution

derivative of

e^{2} + (sec (x) x)

Solution

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

Solution steps

\frac{d}{d x} (e^{2} + sec (x) x)

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (e^{2}) = 0

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

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

Simplify

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

Graph

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d er i v a t i v e \frac{( 3 x ^{2} + x )}{( 3 x ^{2} - x )}

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Frequently Asked Questions (FAQ)

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