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Derivative of secx tanx

TopIn trigonometry, we will study about different types of functions. Here, we will see the different types of derivatives of trigonometric functions.

Let us see the different types of derivatives of inverse in the trigonometric functions:

$\frac{d}{du}$ sin (u) = cos (u)

$\frac{d}{du}$ cos (u) = - sin (u)

$\frac{d}{du}$ tan (u) = sec2 (u)

$\frac{d}{du}$ csc (u) = - csc (u) cot (u)

$\frac{d}{du}$ sec (u) = sec (u) tan (u)

$\frac{d}{du}$ cot (u) = - csc2 (u)

Now, we will see the derivative of sec x tan x and see how to prove the derivative of sec x tan x.

The derivative of Sec x Tan x is sec (x) (tan2(x) + sec2 (x)). Here, we will see the proof of the derivative of Sec x Tan x.

First, write the given function in the derivative form as follows:

$\frac{d}{du}$ sec x tan x = sec (x) (tan2(x) + sec2 (x))

Here, we have to follow the product rule for finding the derivative of the given function.

The product rule is given by:

(u v)' = uv' + u'v

Here, the value of u is sec (x) and the value of v = tan (x).

Put these values in the product rule. So, we can write it as follows:

$\frac{d}{dx}$ sec x tan x = sec x $\frac{d}{dx}$ tan x + tan x $\frac{d}{dx}$ sec x

If we differentiate tan x with respect to x, we get sec2 x and the differentiation of sec x is sec x tan x.

So, we can write it as follows:

sec x3 + tan (x) (tan (x) sec (x))

Or, we can write it as follows:

sec (x) (tan2(x) + sec2 (x))

So, the derivative of sec x tan x is sec (x) (tan2(x) + sec2 (x))