Question

D/dx( secsqrt x -tansqrt x)=

Answer 1

Answer:

$\frac{d}{dx} ( \sec {}^{2} x) - \frac{d}{dx} ( \tan {}^{2} x) \\ 2 \sec {}^{2} x \tan \: x - 2 \tan \: x \sec {}^{2} x = 0$

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Answer 2

Answer:

The derivative of given function $\frac{d}{dx}(sec^2x-tan^2x)=0$

Step-by-step explanation:

Here given function $f(x)$ is  $(sec^2x-tan^2x)$.

On differentiate given function with respect to $x$.

                 $\frac{d}{dx}f(x) =\frac{d}{dx}(sec^2x-tan^2x)$

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

                             $=2secx\frac{d}{dx}secx-2tanx\frac{d}{dx}tanx$

                             $=2secxtanxsecx-2tanxsec^2x\\=2sec^2xtanx-2sec^2xtanx\\=0$

But As we know the identity

                              $1+tan^2x = sec^2x\\sec^2x-tan^2x=1$

Hence the given function is a constant function.

Therefore, the derivative of function f(x) is $sec^2x-tan^2x$ is zero.