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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - 2 tan (x) sec^{2} (x)

Simplify

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

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