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Differentiate the function.
$ y = \tan [\ln (ax + b)] $
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00:33
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 6
Derivatives of Logarithmic Functions
Derivatives
Differentiation
University of Michigan - Ann Arbor
University of Nottingham
Idaho State 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.
01:10
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02:14
This problem were to find derivative tangent of natural log of x, plus b, so the outer function after oppression here is tangent and inner 1 is natural law. So why checking derivative we're going to start from the outer 1 thereat of tangent is secant squared of natural log of x, plus b. Now we're going to multiply this by derivative of the inner operation or inner function, which is natural log of a of p. We know that this is equal to 1 over a x plus b times an so. The answer is that second spread of natural log of x, plus, b times a divided by a x plus b, were actually we can take this constant and write it here. Southat, for the answer would be a times: secant square of natural log of x, plus b, divided by a times x, plus b,
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