Differentiate the function y = (x^2)/(3x-1) with respect to x.
This requires use of the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)^2]dy/dx = ([(3x-1)*2x] - 3x^2)/[(3x-1)^2],= (3x^2-2x)/[(3x-1)^2],=[x(3x-2)]/[(3x-1)^2]
TS
Related Maths A Level answers
All answers ▸How do you find the minimum of the equation sin^2(x) + 4sin(x)?
By first proving that sin2θ=2sinθcosθ, calculate ∫1+sinθcosθ dθ.
If z is a complex number, solve the equation (z+i)* = 2iz+1 where the star (*) denotes the complex conjugate.
The function f has domain (-∞, 0) and is defines as f(x) = (x^2 + 2)/(x^2 + 5) (here ^ is used to represent a power). Show that f'(x) < 0. What is the range of f?