Differentiation: (lesson 1 of 3)

## Common derivatives formulas - exercises

### Rules for Common Derivatives

**f(x) and g(x) are differentiable functions, C is real number:**

**1. Constant-Multiple Rule**

**2. Sum Rule **

### Derivatives of Polynomials

**1.**

Example 1:

**2.**

**3. **

Example 2:

Example 3:

Example 4:

Find the derivative of y = 7 x^{4}

Solution:

Example 5:

Find the derivative of y = 2 x^{3} - 4 x^{2} + 3 x - 5

Solution:

### Derivative of Trigonometric functions

**1. **

**2. **

**3. **

**4. **

Example 6:

Find the derivative of y = 3x + sin(x) - 4cos(x)

Solution 6:

### Derivatives of Inverse Trigonometric Functions

**1. **

**2. **

**3. **

**4. **

Example 7:

Find the derivative of y = arcsin(x) - 2arctan(x) + arcctg(x)

Solution 7:

### Derivatives of Exponential and Logarithmic Functions

**1. **

**2. **

**3. **

**4. **

Example 8:

Find the derivative of y = 3ln(x) - 4e^{x}

Solution 8: