Why does ln(x) differentiate to 1/x ?
At first glance, this may seem quite complicated. However, it is simple once you make use of exponents.
Let y=ln(x).
This can be written as: ey = eln(x)
e to the power of a natural log cancels out, which gives:
ey=x
Differentiating both sides with respect to x gives:
ey (dy/dx)=1
[This uses implicit differentiation. Remember that you must multiply ey by dy/dx as there isn't an x on that side]
Substituting in ey=x gives:
x (dy/dx) =1
And so dy/dx = 1/x
CE
Related Maths A Level answers
All answers ▸The equation of a circle is x^2+y^2-6x-4y+4=0. i) Find the radius and centre of the circle. ii) Find the coordinates of the points of intersection with the line y=x+2
How do you find the gradient of a line at a certain point when f(x) is in the form of a fraction, where both the numerator and denominator are functions of x?
The line l1 has equation 4y - 3x = 10. Line l2 passes through points (5, -1) and (-1, 8). Determine whether the lines l1 and l2 are parallel, perpendicular or neither.
Express (x + 1)/((x^2)*(2x – 1)) in partial fractions