What is the derivative of 1/((1+sec(x)^2)) ?

The derivative of 1/((1+sec(x)^2)) is -(sin(2x))/((1+cos(x))^3)

What is the first derivative of 1/((1+sec(x)^2)) ?

The first derivative of 1/((1+sec(x)^2)) is -(sin(2x))/((1+cos(x))^3)

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

- \frac{sin ( 2 x )}{( 1 + cos ( x ) ) ^{3}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{2}{( 1 + sec ( x ) ) ^{3}} \frac{d}{d x} (1 + sec (x))

= - \frac{2}{( 1 + sec ( x ) ) ^{3}} \frac{d}{d x} (1 + sec (x))

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

= - \frac{2}{( 1 + sec ( x ) ) ^{3}} sec (x) tan (x)

Simplify

- \frac{2}{( 1 + sec ( x ) ) ^{3}} sec (x) tan (x) : - \frac{sin ( 2 x )}{( 1 + cos ( x ) ) ^{3}}

= - \frac{sin ( 2 x )}{( 1 + cos ( x ) ) ^{3}}

\frac{\partial}{\partial x} (3 x y - 5 x^{2} y)

\int e^{x} tan^{2} (e^{x}) d x

\int \frac{5}{x ( x - 5 ) ^{2}} d x

f (t) = sin (4 t)

x \to π lim (x sec (x))

What is the derivative of 1/((1+sec(x)^2)) ?
The derivative of 1/((1+sec(x)^2)) is -(sin(2x))/((1+cos(x))^3)
What is the first derivative of 1/((1+sec(x)^2)) ?
The first derivative of 1/((1+sec(x)^2)) is -(sin(2x))/((1+cos(x))^3)