Verified answer

f'(x)= 4· 1/(2x+5·lnx) · (2+5/x)

f'(5)= 4· 1/(10+5·ln5) ·3 = 12/(10+5·ln5) ~0,6649...

saludos

f (x) = 4 ln [ 2x + 5 ln x ]

f '(x) = 4 [ 2x + 5 ln x ] ' / [ 2x + 5 ln x ]

f '(x) = 4 [ 2 + 5/x ] / [ 2x + 5 ln x ]

f '(x) = 4 [ (2x + 5) / x ] / [ 2x + 5 ln x ]

f '(x) = 4 [ 2x + 5 ] / [ 2x² + 5x ln x ]

f '(x) = [ 8x + 20 ] / [ 2x² + 5x ln x ]

<=>

f '(5) = [ 40 + 20 ] / [ 50 + 25 ln 5 ]

f '(5) = (60) / (50 + 25 ln 5)

f '(5) = (12) / (10 + 5 ln 5)

f '(5) ~ 0.6649

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f '(x) = 4(2 + 5/x)/(2x + 5lnx) ----->f '(5) = 12/(10+ 5ln5)