y = arcsec(x), Find dy/dx.
The key to this problem is to apply sec to both sides, and then differentiate implicitly: sec(y)=x; dsec(y)/dx = 1; tan(y)sec(y)dy/dx = 1; dy/dx = 1/(tan(y)sec(y)). Then using the fact that sec(y)=x and tan2x + 1 = sec2x, we can rewrite our derivative in terms of x only: dy/dx = 1/(x√(x2-1))
NY
Related Maths A Level answers
All answers ▸Find the gradient at x=1 for the curve y=2x*e^2x
Find the integral of 4x^2 - 10x + 1/(x^(1/2)), with respect to x, in its simplest form.
How does finding the gradient of a line and the area under a graph relate to real world problems?
How do I differentiate f(x) = cos(x)/x?