If y = ln(u(x)), dy/dx = ?

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Multiple Choice

If y = ln(u(x)), dy/dx = ?

Explanation:
The derivative of a natural logarithm chain follows the chain rule: d/dx [ln(u(x))] = (1/u(x)) · u'(x). Here the inner function is u(x) and its derivative is u'(x). So dy/dx = u'(x)/u(x). This is valid wherever u(x) > 0 so ln(u(x)) is defined. The other forms don’t match the chain-rule result for the derivative of ln(u(x)).

The derivative of a natural logarithm chain follows the chain rule: d/dx [ln(u(x))] = (1/u(x)) · u'(x). Here the inner function is u(x) and its derivative is u'(x). So dy/dx = u'(x)/u(x). This is valid wherever u(x) > 0 so ln(u(x)) is defined. The other forms don’t match the chain-rule result for the derivative of ln(u(x)).

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