Answer:
[tex]y = \cos[\ln x + \ln (5\cdot x - 2)]\cdot \left(\frac{1}{x} + \frac{5}{5\cdot x-2} \right)[/tex]
Explanation:
Let [tex]y = \sin[\ln(5\cdot x^{2}-2\cdot x)][/tex] and we proceed to find the derivative by the following steps:
1) [tex]y = \sin[\ln(5\cdot x^{2}-2\cdot x)][/tex] Given
2) [tex]y = \sin [\ln[x\cdot (5\cdot x - 2)]][/tex] Distributive property
3) [tex]y = \sin[\ln x + \ln (5\cdot x - 2 )][/tex] [tex]\ln (a\cdot b) = \ln a + \ln b[/tex]
4) [tex]y = \cos[\ln x + \ln (5\cdot x - 2)]\cdot \left(\frac{1}{x} + \frac{5}{5\cdot x-2} \right)[/tex] [tex]\frac{d}{dx} (\sin x) = \cos x[/tex]/[tex]\frac{d}{dx}(\ln x) = \frac{1}{x}[/tex]/[tex]\frac{d}{dx}(c\cdot x^{n}) = n\cdot c\cdot x^{n-1}[/tex]/Rule of chain/Result
