Product and Quotient Rule for Derivatives »

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

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Example 1:

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Example 2:

Example 3:

Example 4:

Find the derivative of y = 7 x⁴

Solution:

Example 5:

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

Solution:

Derivative of Trigonometric functions

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Example 6:

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

Solution 6:

Derivatives of Inverse Trigonometric Functions

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Example 7:

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

Solution 7:

Derivatives of Exponential and Logarithmic Functions

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Example 8:

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

Solution 8: