At the end of this section students should be able to:

  1. find the derivative of \(e^{f(x)}\) , where \(f(x)\) is a differentiable function of \(x\);
  2. find the derivative of \(\ln ⁡f(x)\) (to include functions of \(x\) – polynomials or trigonometric);
  3. apply the chain rule to obtain gradients and equations of tangents and normals to curves given by their parametric equations;
  4. use the concept of implicit differentiation, with the assumption that one of the variables is a function of the other;
  5. differentiate any combinations of polynomials, trigonometric, exponential and logarithmic functions;
  6. differentiate inverse trigonometric functions
  7. obtain second derivatives, \(f''(x)\), of the functions in 3, 4, 5 above;
  8. find the first and second partial derivatives of \(u=f(x, y)\).