Proofs of Common Derivatives

Derivatives are a fundamental concept in calculus, allowing us to study the rates of change and the slopes of curves. Understanding the derivatives of common mathematical functions is essential for solving a wide range of problems in science, engineering, and economics. In this section, we will explore the proofs of the derivatives of various functions, providing step-by-step explanations and justifications for each derivative rule.

Derivative of abs(x) - Proof and Explanation

Derivative of acos(x) - Proof and Explanation

Derivative of acosh(x) - Proof and Explanation

Derivative of asin(x) - Proof and Explanation

Derivative of asinh(x) - Proof and Explanation

Derivative of atan(x) - Proof and Explanation

Derivative of atanh(x) - Proof and Explanation

Derivative of cos(x) - Proof and Explanation

Derivative of cosh(x) - Proof and Explanation

Derivative of cot(x) - Proof and Explanation

Derivative of coth(x) - Proof and Explanation

Derivative of csc(x) - Proof and Explanation

Derivative of log(x) - Proof and Explanation

Derivative of sec(x) - Proof and Explanation

Derivative of sin(x) - Proof and Explanation

Derivative of sinh(x) - Proof and Explanation

Derivative of tan(x) - Proof and Explanation

Derivative of tanh(x) - Proof and Explanation

Derivative of the Square Root sqrt(x) - Proof and Explanation