# How do you find #(d^2y)/(dx^2)# given #x=tany#?

##### 2 Answers

#### Explanation:

**Case : 1**

Since,

**Case : 2**

Thus, in this Case,

**Case : 1**

Thus,

To differentiate without using the inverse tangent, see below.

#### Explanation:

Differentiate both sides with respect to

Differentiate again w.r.t.

Now rfeplace

**To see that this is the same as the other answer**

(To see this draw and label a right triangle with angle

(Or use

Now,

# = -2 siny/cosy cos^4y#

# = -2tany (cos^2y)^2#

# = -2 x 1/(1+x^2)^2#

# = (-2x)/(1+x^2)^2# .