Find the derivative of f(x)=exp((tanx)^(1/2))
We use the chain rule. Let u(x)=exp(x), v(x)=x1/2, w(x) = tan(x).
Then f(x) = u(v(w(x))). So by the chain rule, f'(x) = u'(v(w(x)))*(v(w(x)))'.
u'(x) = exp(x).
By the chain rule, (v(w(x)))' = v'(w(x))w'(x).
v'(x) = x-1/2/2w'(x)= sec2(x)
So f'(x) = exp((tan(x)1/2))(cos(x)/2)
LD
Related Maths A Level answers
All answers ▸Use simultaneous equations to find the points where the following lines cross: 3x - y = 4 and x^2 + 7y = 5
A level Maths question - The graph of y=2sin(2x)+1 is rotated 360 degrees about the x-axis to form a solid. Find the volume enclosed by the curve, the co-ordinate axes and the line x=pi/2
f(x) = 2x^3 – 7x^2 + 4x + 4 (a) Use the factor theorem to show that (x – 2) is a factor of f(x). (2) (b) Factorise f(x) completely.
Find the surface area of a hand held fan (modeled with negligible depth) with radius 8 cm and a 60 degree angle at the centre