Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Test Prep Workbook Update
5th Edition
ISBN: 9780328909148
Author: Prentice Hall
Publisher: Prentice Hall
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How to use logarithmic differentiation for this?
Name
2. Use the logarithmic differentiation to simplify completely before finding the
derivative.
Math 2413
(3x-4) (4x'+1)*
(5x+2)'
Section 3.9
y =
Do not write answer as a single fraction.
Show all work for full credit. Factor answers completely. No negative exponents, no
complex fractions in final answer
1. Differentiate the following functions.
A. y=In(cos (x))
B. y= log,(5x-1)
C. y=4-3*
In(x)
D. y=(sin(x))" Note: Use logarithmic differentiation
71 - 75: Use logarithmic differentiation to find the derivative of each function.
74. y =
V z+1
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- EVALUATION Find the derivative of the given function. Fill the missing expressions. Use logarithmic differentiation. y = x· secx · Vx² + 1 Step 1. Take the absolute value of both sides. lyl = |x - secx · Jx2 + 1 Step 2. Take the natural logarithm of both sides. In ]y| = In x• secx · x2 + 1 Step 3. Expand using the properties of Logarithm Inlyl = Inx + In|secx| + Step 4. Differentiate both sides. D,(In\y\) = Dx Inx + In|secx| +In(x² + 1) 1 1 = -+ .· Dz(secx) + 1 Dz(x² + 1) 2 x2 + 1 1 1 · secx tanx +: 1 2x 2 x2 + 1 Step 5. Multiply both sides of the equation by y to solve for y' + tanx + (x² + 1) Step 6. Substitute y with the given function. 1 y' = + 5cotx + \3(x+ 1) (1 – x²).arrow_forwardUse logarithmic differentiation to find the derivative of y = sin(5x)1+5x y = 5*(1+5*x)*sin Your last answer was interpreted as follows: 5*(1+5*x)*sin This answer is invalid. Forbidden variable or constant: sin. Checkarrow_forwardPls help ASAParrow_forward
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