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.

31. y=arccot(√t)

Accepted Answer

Welcome back everyone. Find dyy divided by dx, given that y equals inverse of tangent of the square root of x. For this problem, we want to find the derivative of y with respect to x, and we have to notice that this is a composite function. So we are going to apply the chain rule. According to the channel, we take the derivative of the outer function which is inverse of tangent of square root of x, and we want to differentiate with respect to the inner function. So with respect to square root of x, followed by multiplication of the derivative. I'm sorry, by the derivative of the inner function. So the derivative of the square root of x with respect to x. Notice that we want to identify two derivatives. Let's remember that the derivative of inverse of tangent of x is equal to 1 divided by 1 + x2. So in this case if we are looking for the derivative of inverse of tangent of the square root of x, that would be 1 divided by 1 plus square root of x squared, right, if we are differentiating with respect to square root of x, and this is equal to 1 divided by 1 plus x. From here we want to find the derivative of square root of x. And we can rewrite it as x is the power of 1/2. So we can apply the power rule that would be 1/2 x to the power of 1/2 minus 1. Which is 1/2 x the power of -1/22. We can rewrite it as 1 divided by 2 square root of x and combine the results. So that the derivative of y with respect to x is equal to. 1 divided by 1 plus x, that's our first derivative multiplied by 1 divided by 2 square root of x. Combining, we get a 1 divided by 2 square root of x multiplied by 1 plus x, and that's 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.31. y=arccot(√t)

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