Differentiate w.r.t x the expression arccos(x).
Using implicit differentiation, let y equal arccos(x) : y=arccos(x). So x = cos(y), and dx/dy = -sin(y). dy/dx is therefore -1/sin(y). from trig indentities: sin(y) = sqrt(1-cos^2(y)). Substituting gives dy/dx = -1/sqrt(cos^2(y)) which is the derivative of arccos.
DP
Answered by Daniel P. • Further Mathematics tutor
5412 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Let I(n) = integral from 1 to e of (ln(x)^n)/(x^2) dx where n is a natural number. Firstly find I(0). Show that I(n) = -(1/e) + n*I(n-1). Using this formula find I(1).
Find the square root of complex number 3 + 4i
Prove by induction that 11^n - 6 is divisible by 5 for all positive integer n.
Find the eigenvalues and eigenvectors of the following 3x3 matrix (reading left to right, top to bottom): (1 0 2 3 1 1 2 0 1)