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Popular >

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

Solution

derivative of

- 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 )}

Popular Examples

tangent of x/(x^2+25)tangent of

\frac{x}{x ^{2} + 25}

derivative of arctan(ax)

\frac{d}{d x} (arctan (a x))

integral of (2x^{-3})

\int (2 x^{- 3}) d x

derivative of ((x^2-1(x+1))/(x^2-2x+1))

\frac{d}{d x} (\frac{( x ^{2} - 1 ) ( x + 1 )}{x ^{2} - 2 x + 1})

integral of (e^x)/((1+e^x)^2)

\int \frac{e ^{x}}{( 1 + e ^{x} ) ^{2}} d x

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))