In Exercises 21–48, find the derivative of y with respect to t...

Question

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

43. y=√(arcsin x)

Accepted Answer

Welcome back everyone. Find d y divided by dx, given that y equals inverse of sin of x raised to the power of 1/3. For this problem we want to find the derivative of y with respect to x, and we have to notice that y is a composite function. So we are going to apply the chain rule. We are going to take our outer function, inverse of sin of x, raise to the power of 1/3. And we're going to differentiate it with respect to the inner function which is inverse. Of sign of acts. And according to the chain rule we want to multiply by the derivative of the inner function inverse of sin of x. With respect to X. So now let's focus on each derivative. For the first derivative, we want to apply the power rule, so we bring down the exponent, which is 1/3. And we decrease the original exponent by 1 unit, so we get 1/3 inverse of sin of x raise to the power of 1/3 minus 1, which is -2/3. For the second derivative, let's remember that the derivative of inverse of sin of x is equal to 1 divided by the square root of 1 minus x 2. And from here we can simplify. We are going to get 1 in the numerator. In the denominator we have 3. Followed by inverse of sin of x raises the power of 2/3 where using the reciprocal rule. Followed by square root of 1 minus x 2, and this is how we get our final derivative for this problem. Thank you for watching.

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.43. y=√(arcsin x)

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In Exercises 21–48, find the derivative of y with respect to the appropriate variable.
43. y=√(arcsin x)