목록

121/1000, derivative of sin^-1(x), implicit differentiation

• bprp calculus b… 27일 전 2026.09.05 16:00 인기
• 2,313
  13

목록

이전글लक्ष्मीकांत स्पेक्ट्रम या UPSC/UPPCS की तैयारी से संबंधित किसी भी बुक को पढ़ने का सही तरीका क्या है?2026.09.05
다음글Crush this Algebra Challenge in seconds #maths2026.09.05
댓글 13

댓글목록



@vikramrawat526… 　27일 전

Day one to one

2026-09-05 19:21

[ytcid:UgzQNf15Gh0rNZvydVl4AaABAg] Day one to one



@ImadAjjaj 　27일 전

121?

2026-09-05 17:41

[ytcid:UgyVj-ZmidWkouiVOLJ4AaABAg] 121?



@BassemFanari 　27일 전

How to find d/dx (sin⁻¹ x) without using θ (or any other variable)
∵  sin(sin⁻¹ x) = x
∴  d/dx sin(sin⁻¹ x) = 1
Differentiating:
⇒  cos(sin⁻¹ x)⋅d/dx (sin⁻¹ x) = 1
⇒  d/dx (sin⁻¹ x) = 1/cos(sin⁻¹ x)
⇒  d/dx (sin⁻¹ x) = 1/√(1–sin²(sin⁻¹ x))
⇒  d/dx (sin⁻¹ x) = 1/√(1–x²)

2026-09-05 16:54

[ytcid:UgyiL0A3VqErSl2sJ4t4AaABAg] How to find d/dx (sin⁻¹ x) without using θ (or any other variable) ∵ sin(sin⁻¹ x) = x ∴ d/dx sin(sin⁻¹ x) = 1 Differentiating: ⇒ cos(sin⁻¹ x)⋅d/dx (sin⁻¹ x) = 1 ⇒ d/dx (sin⁻¹ x) = 1/cos(sin⁻¹ x) ⇒ d/dx (sin⁻¹ x) = 1/√(1–sin²(sin⁻¹ x)) ⇒ d/dx (sin⁻¹ x) = 1/√(1–x²)



@sarin_5063 　27일 전

The reason why cos theta = sqrt(1-x^2) and not +-sqrt(1-x^2):

When you define theta = arcsin x, the range of possible values of theta becomes [-pi/2, pi/2].
For any value of theta in this range, cos theta >= 0. Therefore, the possibility that cos theta = -sqrt(1-x^2) is ruled out.

(This is also the same reason as to why you do not use absolute values when doing trig subs in integration)

2026-09-05 16:54

[ytcid:UgyOE5fQabJviFhnkpx4AaABAg] The reason why cos theta = sqrt(1-x^2) and not +-sqrt(1-x^2): When you define theta = arcsin x, the range of possible values of theta becomes [-pi/2, pi/2]. For any value of theta in this range, cos theta >= 0. Therefore, the possibility that cos theta = -sqrt(1-x^2) is ruled out. (This is also the same reason as to why you do not use absolute values when doing trig subs in integration)



@crankykransky2… 　27일 전

Now do it by first principles

2026-09-05 16:13

[ytcid:UgwRZFg2gSzqDOFSIfB4AaABAg] Now do it by first principles



@OyatilloToshma… 　27일 전

Day 121?

2026-09-05 16:07

[ytcid:UgwxsjfjpIjW79LYSGZ4AaABAg] Day 121?



@surenazand 　27일 전

Thank you I learned so much ❤

2026-09-06 03:16

[ytcid:UgxHEqpCcvHbSQwA21V4AaABAg] Thank you I learned so much ❤



@Antonino-f1i 　27일 전

Perfect ???

2026-09-06 02:43

[ytcid:UgxncRkGoq5kPt8R9A94AaABAg] Perfect ???



@_zelatrix 　27일 전

What's stopping me saying that 1/cos x = sec x at the end?

2026-09-05 21:51

[ytcid:UgysXBr2FTg-nNNMi_x4AaABAg] What's stopping me saying that 1/cos x = sec x at the end?



@tionggeegoh986… 　24일 전

this differentiation is only for |x|<½π hence cos theta >0 ie cos theta =√(1-x²)

2026-09-08 15:52

[ytcid:UgzJqYJY0z9aOfDE7e94AaABAg] this differentiation is only for |x|<½π hence cos theta >0 ie cos theta =√(1-x²)