Question

Find the derivative of y = sin(ln(5x2 − 2x))

Answer 1

`y = \cos[\ln x + \ln (5\cdot x - 2)]\cdot \left((1)/(x) + (5)/(5\cdot x-2) \right)`

Step-by-step explanation:

Let
`y = \sin[\ln(5\cdot x^(2)-2\cdot x)]` and we proceed to find the derivative by the following steps:

1)
`y = \sin[\ln(5\cdot x^(2)-2\cdot x)]` Given

2)
`y = \sin [\ln[x\cdot (5\cdot x - 2)]]` Distributive property

3)
`y = \sin[\ln x + \ln (5\cdot x - 2 )]`
`\ln (a\cdot b) = \ln a + \ln b`

4)
`y = \cos[\ln x + \ln (5\cdot x - 2)]\cdot \left((1)/(x) + (5)/(5\cdot x-2) \right)`
`(d)/(dx) (\sin x) = \cos x`/
`(d)/(dx)(\ln x) = (1)/(x)`/
`(d)/(dx)(c\cdot x^(n)) = n\cdot c\cdot x^(n-1)`/Rule of chain/Result