What is the derivative of (sec(x+tan(x))^{-3}) ?

The derivative of (sec(x+tan(x))^{-3}) is 3/((sec(x)+tan(x))^4(-1+sin(x)))

What is the first derivative of (sec(x+tan(x))^{-3}) ?

The first derivative of (sec(x+tan(x))^{-3}) is 3/((sec(x)+tan(x))^4(-1+sin(x)))

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

\frac{3}{( sec ( x ) + tan ( x ) ) ^{4} ( - 1 + sin ( x ) )}

Solution steps

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

Apply the chain rule:

- \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} \frac{d}{d x} (sec (x) + tan (x))

= - \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} \frac{d}{d x} (sec (x) + tan (x))

\frac{d}{d x} (sec (x) + tan (x)) = - \frac{1}{- 1 + sin ( x )}

= - \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} (- \frac{1}{- 1 + sin ( x )})

Simplify

- \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} (- \frac{1}{- 1 + sin ( x )}) : \frac{3}{( sec ( x ) + tan ( x ) ) ^{4} ( - 1 + sin ( x ) )}

= \frac{3}{( sec ( x ) + tan ( x ) ) ^{4} ( - 1 + sin ( x ) )}

\int_{0}^{4} 5 x d x

x \to 0 + lim (ln (tan (x)))

\frac{d}{d x} (arcsec (x) - 7 x)

\int \frac{1}{2 y - y ^{2}} d y

y = 2 x^{3} - 5 x + 1, (- 1, 4)

What is the derivative of (sec(x+tan(x))^{-3}) ?
The derivative of (sec(x+tan(x))^{-3}) is 3/((sec(x)+tan(x))^4(-1+sin(x)))
What is the first derivative of (sec(x+tan(x))^{-3}) ?
The first derivative of (sec(x+tan(x))^{-3}) is 3/((sec(x)+tan(x))^4(-1+sin(x)))