2. y = ln x Can be written as y x = e y Differentiating dx/dx = e dy/dx y 1 = e dy/dx y dy/dx = 1/ e = 1/x
3. xDifferentiate y = x Ln y = x ln x 1/y dy/dx = x (1/x) + ln x (y) 1/y dy/dx = ( 1 + ln x) dy/dx = y ( 1 + ln x) x dy/dx = x ( 1 + ln x)
4. 2 4x Differentiate y = a To differentiate we use the formula u = u d/dx a a du/dx
5. Continued from slide 5 2 Let u = 4x du/dx = 8x Applying the formula we obtain 2 2 4x 4x dy/dx = a * 8x * ln a = 8x ln a * a
6. 8x Differentiate y = 2 Solution to find dy/dx we use the differentiation formula u u d/dx a = a du/dxln a Let a = 2, u = 8x, then du/dx = 8 Applying the formula we obtain 8x dy/dx= 2 * 8 * ln 2