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Find the derivative of the function. Simplify where possible.$ y = \cos^{-1} (\sin^{-1} t) $
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00:55
Frank Lin
Doruk Isik
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 5
Implicit Differentiation
Derivatives
Differentiation
Faith A.
October 1, 2020
Campbell University
Baylor University
Boston College
Lectures
04:40
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
44:57
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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So if this problem we're gonna be utilizing the derivative of inverse trig functions on this will be useful because we use inverse trig functions in math, they come up. So if we want to find the rate of change or the the slope of a tangent line of the graph, then we're gonna want to utilize in verse trig function identities on derivatives. So keep in mind that what we have in this case is the inverse coastline. So why equals the inverse coastline of the inverse sign of key? It could be acts, but in this case, it's teeth. All right, that's what we have. Remember that the derivative of the inverse coastline is one is negative. One over the square root of one minus X squared, where X is what's inside the parentheses. So now it will end up getting. Is that why crime is equal to negative one over the square root of one minus sine inverse of tea square? Yeah, And then, since we have to do change rule here, we're gonna multiplying that by the derivative of what's inside the parentheses, which that's another trick function in verse, trick function. That will be one over the square root of one minus. He squared because that's what happens when you take the derivative of the inverse sign of tea. Then we can multiply all this together to simplify it further. What will end up getting as a result is why prime being equal Thio negative one over the square root of one. Basically everything we see here. Uh, the only difference is we can just copy and paste this thing. Only difference is now we can multiply this bottom portion, uh, at the bottom. So we'll have times That's right here. And that will be our final answer for the derivative of why?
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