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.

21. y=arccos(x²)

Accepted Answer

Welcome back everyone. Find the derivative of y given that y equals inverse of sin of 2 x cubed. For this problem, since we have a composite function, we want to apply the chain rule. So d y divided by d x is going to be the derivative of the outer function, which is. Inverse of sine of 2 x cubed with respect to the inner function. So 2 x cubed and according to the chain rule we're multiplying by the derivative of the inner function 2 x cubed. With respect to X. So let's find each derivative. For the first one, let's remember the derivative of inverse of sign. That's one divided by a square root of. 1 minus the square of the inner function and in this case our inner function is 2 x cubed. And the derivative of 2 x cubed can be found using the power rule. We can factor out 2, and applying the power rule for x cubed, we're going to get 3. We're bringing down the exponent x to the power of 23 minus 1 gives us 2, right? And now what we can do is simplify. 2 multiplied by 3 is 6, so we get 6 x squared in the numerator. And in the denominator we're going to write square root of 1 minus 224 x cubed square x to the power of 3 multiplied by 2, which is 6. So square root of 1 minus 4 x to the power of 6, and this is our final answer for this problem. Thank you for watching.

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.21. y=arccos(x²)

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In Exercises 21–48, find the derivative of y with respect to the appropriate variable.
21. y=arccos(x²)