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Find the derivative. Simplify where possible.$ y = x \tanh^{-1}x + \ln \sqrt {1 - x^2} $
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Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 11
Hyperbolic Functions
Derivatives
Differentiation
Missouri State University
Oregon State University
University of Nottingham
Idaho State University
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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we know that 10 h the negative one of you. In other words, inverse tangent is you prime over one month's you square. Therefore, we can write this as one nice x squared plus negative access just minus X over one minus X squared. And this simplifies to tangent h the negative one of acts. So that's the inverse.
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