Evaluate the derivative of the following functions.
f(u)...

Question

Evaluate the derivative of the following functions.

f(u) = csc^-1 (2u + 1)

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Find the derivative of FA T is equal to the inverse cosicant of 5T minus 13. Awesome. So, it appears what we're ultimately trying to solve for is we're trying to figure out what the derivative of FAT is. So we're trying to find the first derivative of this function of FAT. So with that said, We need to first off, we need to figure out the derivative of this inverse cosicant function. So you need to take D by DX, which is a fancy way of saying we're taking the derivative with respect to X. Of cos so inverse cosicants, we need to take inverse cosicant of X, which is equal to, as we should recall, negative 1 divided by the absolute value of X multiplied by the square root of X2 minus 1. Fantastic. So now, let us state or let us let the variable U equal 5 T minus 13, and when we allow you to be that expression, we'll be able to easily write that D by DT, so now we're taking the derivative with respect to T. Of inverse cosicant of U is equal to -1 divided by the absolute value of U multiplied by the square root of U squared minus 1 multiplied by DU by DT. Fantastic. So now, we need to take D by DT, so we're taking the derivative with respect to T of inverse cosicant of 5 T minus 13. is equal to -1 divided by the absolute value of 5T minus 13 multiplied by the square root of 5T. Minus 1321. Multiplied by D by DT. Of 5 minus. 13, fantastic. So it's 5 T minus 13. And when we do a little bit of simplifying, we will find that our final answer will be equal to negative. 5 divided by the absolute value of 5T minus 13, multiplied by the square root of 5T minus 13 squared. -1 And that's it. That is our final answer. Hooray, we did it. So to quickly recap here, Our final answer for the derivative of FAT is negative 5 divided by the absolute value of 5T minus 13, multiplied by the square root of 5T minus 13 squad minus 1. Thank you so much for watching. Hopefully that helped, and I can't wait to see you on the next video. Bye.

Evaluate the derivative of the following functions.
f(u) = csc^-1 (2u + 1)

Key Concepts

Inverse Trigonometric Functions

Chain Rule

Derivative of Inverse Functions

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