Question 7(a)
[Maximum number: 3]
The equation of a curve is .
Find the exact values of x when the gradient of the curve is .
CAIE A-Level Mathematics 3.4.1 Advanced Differentiation
Practise differentiating eˣ, ln x, trigonometric and inverse-tangent composites and applying exact derivative equations to find gradients, coordinates and stationary points.
How this is tested
- differentiate eᵘ, ln u, tan u or tan⁻¹u and retain the derivative of the inner function
- combine advanced derivatives with product or quotient rules before simplifying
- set dy/dx to zero or a stated gradient and solve for exact coordinates or parameters