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Derivative of Tan Squared x?

TopIn the Trigonometry we will concern the different type’s trigonometric function. Here we will see how to determine the derivative of Tan Squared X. As we know, the derivative of Tan Squared X is 2 x tan (x) sec2 (x). Now we will see the prove of the derivative of Tan Squared X.
To find the derivative of Tan Squared X first we have to write the function tan2 x in the derivative form:
So we can write it as:

= $\frac{d}{dx}$ tan2 x = 2 tan x sec2 x;

We known that the derivative of tan x is sec2 x but we solve it using the Chain Rule.

Now use the chain rule, $\frac{d}{dx}$ (tan2 (x)) =

$\frac{d}{dx}$ u

, where the value of u = tan (x) and

$\frac{du}{dx}$ = sec2 x

2u;

So put these values in the trigonometric function:

On putting these values we get:

= X (2 tan (x) ($\frac{du}{dx}$ (tan (x)));

We already know that if we differentiate tan x then we get sec2 x, so put sec2 x in the above function.

= X (2 tan (x) (sec2 (x)));

After differentiating the trigonometric function we get:

= 2 X tan x sec2 (x);

This is how one can solve the derivative of derivative Of Tan Squared X. Let’s see an example to solve the derivative of other trigonometric function. Suppose a function is given f (s) = s2 sin (6x); then we have to find the inverse derivative of a given function.

By using Product rule we get.

u.v = u $\frac{du}{dx}$ v + v. $\frac{du}{dx}$ u;

So we can write as:

$\frac{d}{ds}$ f (s) = $\frac{d}{ds}$ (s2 sin 6x)

= sin 6x $\frac{d}{ds}$ (s2)

(sin (6s));
If we differentiate the value s2then we get 2s and we differentiate sin 6s then we get 6 cos 6s;
Now putting these values in the given function we get:
f (s) = 2s.sin (6s) +s2 . 6(cos (6s));
We can also write it as:
f (s) = 2s.sin (6s) + 6s2 6(cos (6s));
This is how to calculate the inverse Derivatives of trigonometric function.