What is the derivative of-1/(cos^2(x)) ?

The derivative of-1/(cos^2(x)) is -2sec^2(x)tan(x)

What is the first derivative of-1/(cos^2(x)) ?

The first derivative of-1/(cos^2(x)) is -2sec^2(x)tan(x)

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

- 2 sec^{2} (x) tan (x)

Solution steps

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

Simplify

- \frac{1}{cos ^{2} ( x )} : - sec^{2} (x)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

2 sec (x) \frac{d}{d x} (sec (x))

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

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

= - 2 sec (x) sec (x) tan (x)

Simplify

- 2 sec (x) sec (x) tan (x) : - 2 sec^{2} (x) tan (x)

= - 2 sec^{2} (x) tan (x)

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