The function f is defined for x > 0 by f (x) = x^1n x. Obtain an expression for f ′ (x).
By taking the natural log on both sides we can see that: ln(f(x)) = ln(x)^2 This is a more familiar expression that we know how to differentiate LHS: f '(x)/f(x), RHS: 2*ln(x)/x By rearranging this we can see that f '(x) = f(x)2ln(x)/x Substituting our original f(x) expression back into this we find that: f '(x) = x^ln(x)2ln(x)/x = x^(ln(x)-1)2ln(x).
SE
Answered by Steven E. • Further Mathematics tutor
3205 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.
Show that the set of real diagonal (n by n) matrices (with non-zero diagonal elements) represent a group under matrix multiplication
A line has Cartesian equations x−p = (y+2)/q = 3−z and a plane has equation r ∙ [1,−1,−2] = −3. In the case where the angle θ between the line and the plane satisfies sinθ=1/√6 and the line intersects the plane at z = 0. Find p and q.
Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)