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Find the derivative: f(x) = ln ( x x 2 1 ) 2. Differentiate: y = x 3. Find 4. Determine an equation of the tangent line to y = e-3x at (0, 1) 5....

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1. Find the derivative: f(x) = ln ) 1 ( 2 x x 2. Differentiate: y = x tan(x) 3. Find dx dy if x e y + 1 = xy 4. Determine an equation of the tangent line to y = e -3x at (0, 1) 5. Differentiate the implicit function 2ye x + 1 = x 6. Locate any relative extrema and points of inflection for f(x) = x 2 ln(x) 7. Find an equation of the tangent line at the point where x = 2 for the function: y = arctan 2 x 8. Evaluate dx x e 1 2 1 1 9. Evaluate dx x x 13 6 5 2 10. Evaluate dx x e e 2 1 11. Evaluate: dx e e x x 1 4 2
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12. Evaluate dx x x x 1 3 3 3 2 2 13. Without graphing the function, explain how you would determine whether f(x) = 3 2 x is 1-1. 14. Solve: 3e -2x = 6 15. Solve: ln(x) + ln(x-3) = 0
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2.docx

f ' ( x )= 1) d
( ln ( x+ √ x 2+ 1 ) )
dx
1
∗d
x+ √ x 2 +1
( x+ √ x 2+ 1 ) ( by chain rule )
¿
dx ( 1 2 √ x +1
¿
∗ 1+
2
dx
x + √ x +1
1 ¿ ¿ 2 ∗d ( x2 +1 ) ) ( by chain rule ) 1...

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