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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

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