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Popular >

derivative of-sec(x+2sec^3(x))

Solution

\frac{d}{d x} (- sec (x) + 2 sec^{3} (x))

Solution

\frac{- sec ( x ) + 6 sec ^{3} ( x )}{cot ( x )}

Solution steps

\frac{d}{d x} (- sec (x) + 2 sec^{3} (x))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (sec (x)) + \frac{d}{d x} (2 sec^{3} (x))

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

\frac{d}{d x} (2 sec^{3} (x)) = 6 sec^{3} (x) tan (x)

= - sec (x) tan (x) + 6 sec^{3} (x) tan (x)

Rewrite using trig identities

= \frac{- sec ( x ) + 6 sec ^{3} ( x )}{cot ( x )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of-sec(x+2sec^3(x)) ?
The derivative of-sec(x+2sec^3(x)) is (-sec(x)+6sec^3(x))/(cot(x))
What is the first derivative of-sec(x+2sec^3(x)) ?
The first derivative of-sec(x+2sec^3(x)) is (-sec(x)+6sec^3(x))/(cot(x))