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# How to Differentiate Sin^-1?

TopThe inverse Trigonometric Functions are partial inverse Functions for every trigonometric function. The sine Inverse Function is also said to be inverse sine (sin-1) or arcsine (arcsin).

This sine function also satisfies some conditions which are given below:
1. Sin (arcsin p) = p for every value | p | ≤ 1;
2. arcsin (sin p) = p for every value | p | ≤ ⊼ / 2 + k⊼;

Now we will see the representation of inverse trigonometric function:
Function                 Inverse
Sin                          arcsin
Cos                        arccos
Tan                          arctan
Sec                         arcsec
Cosec                    arccosec
Cot                          arccot

Now we will see how to differentiate sin inverse;
Let, y = sin-1(x).
then, x = sin(y) and dx/dy = cos(y)
dy/dx = 1/cos(y)
dy/dx = 1/√(1 - x^2)