Differentiate f.!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

f(x)= (x)/(1-ln(x-6))

Answer 1

f(x) = x / [1 - log(x - 6)]

Apply 'derivative with respect to x' each side.

f'(x) = (d/dx){x / [1 - log(x - 6)]}

The Quotient Rule: (U/V)' = [U'V - UV'] / V²

f'(x) = {x'[1 - log(x - 6)] - x[1 - log(x - 6)]'}/[1 - log(x - 6)]²

Power Rule of Derivative: (d/dx)(xⁿ) = nx^n-1

And derivative of Logarithm Functions: (d/dx)log(x) = 1/x.

f'(x) = {1[1 - log(x - 6)] - x[0 - (1/(x - 6))]}/[1 - log(x - 6)]²

f'(x) = [1 - log(x - 6)  + x/(x - 6)]/[1 - log(x - 6)]²

f'(x) = [x/(x - 6) + 1 - log(x - 6)] / [1 - log(x - 6)]²

Therefore the derivative of f(x) is [x/(x - 6) + 1 - log(x - 6)] / [1 - log(x - 6)]².