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.

23. y=arcsin(√2t)

Accepted Answer

Welcome back everyone. Find the derivative of y given that y equals inverse of cosine of 1/4 x cubed. For this problem, let's write down the derivative as dyy divided by dx. And because y is a composite function, we're going to apply the chain rule. So according to the chain rule, first of all, we want to differentiate the outer function inverse of cosine of 1/4. X cubed with respect to the inner function, right? So the inner function is 1/4 x cubed and then we want to multiply by the derivative of the inner function 1/4. X cubed with respect to X. Now from here let's find each derivative. Now let's remember that the derivative of inverse of cosine is equal to -1. Divided by the square root of 1 minus the square of the inner function, so that would be 1/4 x cubed squared, right. And now for the next term, the derivative of 1/4 x cubed can be found as 1/4 multiplied by. We're going to apply the power rule. The derivative of x cubed is 3 x squared. Now all that we want to do from here is simplify, so we get -1 divided by square root of. 1 minus x to the power of 6. Divided by 16. And we're multiplying by 3/4 X 2. Now let's simplify it further. For the first term we get -1 divided by square root of we can find the common denominator which is 16. In the numerator we are going to have 16 minus x to the power of 6. So 16 minus x the power of 6 divided by 16. And we can basically write 3 x squared in the numerator, and we can add 4 in the denominator, right now the square root of 16 is 4, so we get 4 divided by 4, which gives us 1. We can just eliminate that 16 and we can eliminate 4, and this basically gives us the final answer -3 x 2 divided by the square root of 16 minus x to the power of 6. That's our final answer, and thank you for watching.

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.23. y=arcsin(√2t)

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In Exercises 21–48, find the derivative of y with respect to the appropriate variable.
23. y=arcsin(√2t)