## DIFFERENTIATION

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 $$u=f(x, y)$$.