Math Calculators, Lessons and Formulas

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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

Constant-Multiple Rule

2. Sum Rule

Sum Rule

Derivatives of Polynomials

1. Derivatives of Polynomials

Example 1: Derivative of a Constant Formula

2. Derivatives of Polynomials

3. Derivatives of Polynomials

Example 2: Derivatives of Polynomials Example

Example 3: Derivatives of Polynomials Example


Example 4:

Find the derivative of y = 7 x4

Solution:

Derivatives of Polynomials Solution

Example 5:

Find the derivative of y = 2 x3 - 4 x2 + 3 x - 5

Solution:

Derivatives of Polynomials Solution

Try yourself

exercisie
answer 1 answer 2 answer 3 answer 4

Derivative of Trigonometric functions

1. Derivative of sin(x)

2. Derivative of cos(x)

3. Derivative of tan(x)

4. Derivative of ctg(x)

Example 6:

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

Solution 6:

Derivative of Trigonometric functions

Try yourself

exercisie
answer 1 answer 2 answer 3 answer 4

Derivatives of Inverse Trigonometric Functions

1. Derivative of arcsin(x)

2. Derivative of arccos(x)

3. Derivative of arctan(x)

4. Derivative of arcctg(x)


Example 7:

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

Solution 7:

Derivatives of Inv Trig Function

Try yourself

exercisie
answer 1 answer 2 answer 3 answer 4

Derivatives of Exponential and Logarithmic Functions

1. Derivatives of Exp and Log Functions

2. Derivatives of Exp and Log Functions

3. Derivatives of Exp and Log Functions

4. Derivatives of Exp and Log Functions


Example 8:

Find the derivative of y = 3ln(x) - 4ex

Solution 8:

Derivatives of Exp and Log Functions

Try yourself

exercisie
answer 1 answer 2 answer 3 answer 4