Differentiate 2x/cos(x)
Given that you have a fraction in the question, you are clearly asked to use the quotient rule. In order to do this, you should label the numerator u, and the denominator v, like this: u = 2x v=cos(x). Now, you should differentiate (multiply by the power and subtract 1 from the power) both of these to find u' and v'. For u, which is 2x^1, this is simply a question of removing the x, and so: u' = 2. For v, it is a matter of remembering the derivatives of trigonometric functions. In this case, the differential of cosx, v', is -sinx. And so we have:
u = 2x v = cos(x) u' = 2 v'= -sinx
Now sub all of these into the quotient rule : (vu' - uv')/v^2
This gives us (2cos(x) + 2xsin(x))/cos^2(x)
JS
Related Maths A Level answers
All answers ▸Demonstrate that (2^n)-1 is not a perfect square for any n>2, n ∈ N.
Integrate sin(x)cos(x)^2 from 0 to π/2
Solve 2sin2θ = 1 + cos2θ for 0° ≤ θ ≤ 180°
f(x) = (x-5)/(x^2+5x+4), express this in partial fractions and hence find the integral of f(x) dx between x=0 and x=2, giving the answer as a single simplified logarithm.