Find the first derivative dy/dx of the following. Simplify. DERIVATIVES OF TRIGONOMETRIC, INVERSETRIGONOMETRIC, LOGARITHMIC and EXPONENTIAL FUNCTIONSFind the first derivative dy/dx of the following. Simplify.|1–x3y = In1+ x3WERSITY

Name: Find the first derivative dy/dx of the following. Simplify. DERIVATIVE
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Description: Find the first derivative dy/dx of the following. Simplify. DERIVATIVES OF TRIGONOMETRIC, INVERSETRIGONOMETRIC, LOGARITHMIC and EXPONENTIAL FUNCTIONSFind the first derivative dy/dx of the following. Simplify.|1–x3y = In1+ x3WERSITY

To Find the first derivative dydx of the function and simplify Given the function y = ln 1-x31+x3 y…

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Calculus

Find the first derivative dy/dx of the following. Simplify. 1– x3 y = In 1+ x3

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter6: Rates Of Change

Section6.2: Rates Of Change For Other Functions

Problem 7SBE: Sign of the Derivative: Suppose f=f(x). What is the sign of dfdx in each of the following...

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The Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, the light is absorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensity I at depth x is given by the Beer-Lambert Law: I=I0ekx where I0 is the light intensity at the surface and k is a constant that depends on the murkiness of the water see page 402. A biologist uses a photometer to investigate light penetration in a northern lake, obtaining the data in the table. Light intensity decreases exponentially with depth. Use a graphing calculator to find an exponential function of the form given by the Beer-Lambert Law to model these data. What is the light intensity I0 at the surface on this day, and what is the murkiness constant k for this lake? Hint: If your calculator gives you a function of the form I=abx, convert this to the form you want using the identities bx=eln(bx)=exlnb. See Example 1b. Make a scatter plot of the data, and graph the function that you found in part a on your scatter plot. If the light intensity drops below 0.15 lumen lm, a certain species of algae cant survive because photosynthesis is impossible. Use your model from part a to determine the depth below which there is insufficient light to support this algae. Depth ft Light intensity lm Depth ft Light intensity lm 5 10 15 20 13.0 7.6 4.5 2.7 25 30 35 40 1.8 1.1 0.5 0.3
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