2. Each of the differentiation rules you learned has its differential form counterpoint. For example, given u and v are differentiable functions of x. du = u’dx and dv = v’dx d[uv] = d/dx[uv] dx = [uv’ +vu’]dx = uv’dx + vu’dx =u dv + v du
3.
4. Let’s see how these work: Ex 4, p. 238 Finding differentials Function Derivative Differential
5. Ex 5 p. 239 Finding the differential of a composite function.
6. Ex 6, p.239 Finding the differential of a composite function
7. Differentials can be used to approximate function values. If y = f(x), Then f(x+ Δ x ) ≈ f(x) + dy = f(x) + f’(x)dx The key to using this is to choose a value for x that makes calculations easier.
8. Ex 7 p. 239 Approximating Function Values Use differentials to approximate Solution: Using you can write Using a calculator, ≈ 2.9625
![Each of the differentiation rules you learned has its differential form counterpoint. For example, given u and v are differentiable functions of x. du = u’dx and dv = v’dx d[uv] = d/dx[uv] dx = [uv’ +vu’]dx = uv’dx + vu’dx =u dv + v du](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)