A) Differentiate ln(x) b) integrate ln(x)

A) y=ln(x) Ey = x Ey(dy/dx ) = 1 Eln(x)(dy/dx) = 1 X(dy/dx) = 1 Dy/dx = 1/xb) y = 1 * ln(x) V = ln(x) U= x dv/dx =1/x Du/dx = 1xln(x) - (integral) x * (1/x)xln(x) - (integral) 1= xln(x) -x + C

SR

Related Maths A Level answers

All answers ▸

Let f(x) = 3x^4 - 8x^3 - 3. Find the x- values of the stationary points of this function.


Curves C1 and C2 have equations y= ln(4x-7)+18 and y= a(x^2 +b)^1/2 respectively, where a and b are positive constants. The point P lies on both curves and has x-coordinate 2. It is given that the gradient of C1 at P is equal to the gradient of C2 at P.


y = 4sin(x)cos(3x) . Evaluate dy/dx at the point x = pi.


The curve C has equation y = (x^2 -4x - 2)^2. Point P lies on C and has coordinates (3,N). Find: a) the value of N. b) the equation of the tangent to C at the point P, in the form y=mx+c where m and c are constants to be found. c) determine d^2y/dx^2.