Practice Problem 1. Use differentiation from first principles to find the derivative of f(x)=x at x...

 

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Practice Problem 1. Use differentiation from first principles to find the derivative of f(x)=x² at x = 5. Practice Problems 2. Use first principles to differentiate each of the following functions: (a) y = 4x² - 9x + 1 (b) y= 3. (a) By writing (a + b)² = (a + b)(a + b)² show that (a + b)' = a¹ + 3a²b + 3ab² + b³ (b) Use the result of part (a) to prove that the cube function, x', differentiates to 3x² Practice Problem 1. (a) Verify that the point (1, 2) lies on the curve 2x² + 3y² = 14. (b) By differentiating both sides of 2x² + 3y² = 14 with respect to x, show that dy dx 2x 3y and hence find the gradient of the curve at (1, 2). Practice Problem 1. Use differentiation from first principles to find the derivative of f(x)=x² at x = 5. Practice Problems 2. Use first principles to differentiate each of the following functions: (a) y = 4x² - 9x + 1 (b) y= 3. (a) By writing (a + b)² = (a + b)(a + b)² show that (a + b)' = a¹ + 3a²b + 3ab² + b³ (b) Use the result of part (a) to prove that the cube function, x', differentiates to 3x² Practice Problem 1. (a) Verify that the point (1, 2) lies on the curve 2x² + 3y² = 14. (b) By differentiating both sides of 2x² + 3y² = 14 with respect to x, show that dy dx 2x 3y and hence find the gradient of the curve at (1, 2).