Q:
# What is the derivative of inverse sine?

**The derivative of the inverse sine of x with respect to x is 1/sqrt(1-x^2), where "sqrt" stands for square root.** Inverse sine of x is sometimes written as arcsin(x). By definition, arcsin(x) = -iln(ix + sqrt(1-x^2)), where i is the square root of -1 and ln is the natural logarithm.

One can use the chain rule of differentiation to compute the derivative of inverse sine. The chain rule says that dy/dx = dy/du du/dx. Letting y = arcsin(x) = -iln(ix + sqrt(1-x^2)) = -iln(u) and u = ix + sqrt(1-x^2) gives the result dy/du = -i/u and du/dx = i - x/sqrt(1-x^2). Substituting these results into the chain rule gives d(arcsin(x))/dx = 1/sqrt(1-x^2).

Learn more about Trigonometry-
Q:
## What are the six trig functions?

A: The six trigonometric functions are the sine, cosine, tangent, cosecant, secant and cotangent. The functions are used to find a ratio between the sides of ... Full Answer >Filed Under: -
Q:
## What is the sine of 10 degrees?

A: The sine of a 10-degree angle is 0.17. The sine is defined as the length of the side of the triangle opposite the angle in question, divided by the length ... Full Answer >Filed Under: -
Q:
## How can the equation sin(cos(-1)) be solved?

A: To solve the equation sin(cos(-1)), first it is necessary to solve for cos(-1) and then find the sine of that value. Assuming that (-1) is given in units o... Full Answer >Filed Under: -
Q:
## How do you find the cosine of pi?

A: The trigonometric functions sine, cosine and tangent calculate the ratio of two sides in a right triangle when given an angle in that triangle. To find the... Full Answer >Filed Under: