1)  |
2)  |
3)  |
4)  |
| 5) y = x ln x | 6) y = 5 3x + (3x) 5. |
7)  |
8) y = (x² + 1) 2x . |
9) y = x² e - cot 2x . |
10) y = x sin 5x |
| Calculus I Assignment # 5 |
This assignment covers
Exponential and Log Derivatives
Logarithmic Differentiation
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QUESTIONS
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Find the derivative
| 1) |
2) |
| 3) |
4) |
| 5) y = x ln x | 6) y = 5 3x + (3x) 5. |
| 7) |
8) y = (x² + 1) 2x . |
9) y = x² e - cot 2x . |
10) y = x sin 5x |
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SOLUTIONS
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Find the derivative
| 1) Rewrite f (x) using log rules |
2) Rewrite f (x) using log rules
|
| 3)
|
4) Rewrite f (x) using log rules
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| 5) use logarithmic differentiation it's a variable to a variable exponent. now, y = x ln x t ln y = (ln x) 2 or ln 2 x. |
6) y' = 3(5 3x) ln 5 + 15(3x) 4. |
7)  |
8) use logarithmic differentiation it's a variable to a variable exponent. ln y = 2x ln (x² + 1) so so |
9) we use product rule here y' = 2x e - cot 2x + 2x² csc² 2x e - cot 2x . with some factoring, |
10) use logarithmic differentiation it's a variable to a variable exponent. ln y = sin 5x (ln x) Using product rule again we get so |
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