Differentiate the function or find ππ¦ ππ₯ and simplify the result.
1. π(π₯) = ln(4 + 5π₯)
2. πΉ(π¦) = ln(sin 5π¦)
3. π¦ = ln|π₯3 + 1|
4. π¦ = π₯5(π₯+2)/π₯β3 (by logarithmic differentiation)
5. π¦ = π5x
6. π¦ = πx sin πx
7. π(π₯) = 35x
8. π(π₯) = 4sin2x
9. π(π₯) = sinh π₯2
10. π(π₯) = coth 1/x
Let
Then
By chain rule,
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