Differentiate ln(x)/x

To differentiate this, we use the quotient rule as we have 2 functions of x as a fraction.

The quotient rule states that:

where u is the numerator function and v is the denominator function.

Therefore, u=ln x and v=x.

So:

as that is the derivative of ln x.

And:

as that is the derivative of x.

Substituting these values into the quotient rule equation we have the following answer to this question:


CE

Related Maths A Level answers

All answers ▸

The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) dy/dx (ii) d^2y/dx^2 (3 marks) (b) Verify that C has a stationary point when x = 2 (2marks) (c) Determine the nature of this stationary point, giving a reason for your answer. (2)


Find the gradient of the curve y = x^2(ln(x)) at x = e


Integrate the following equation to find y: dy/dx = 3x^2 + 2x + 6


A girl saves money over 200 weeks. She saves 5p in Week 1, 7p in Week 2, 9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic sequence. Find the amount she saves in Week 200. Calculate total savings over the 200 week period.