How do you find #(d^2y)/(dx^2)# given #x=tany#?
2 Answers
Explanation:
Case : 1
Since,
Case : 2
Thus, in this Case,
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# .