Implicit Differentiation: Step-by-Step Method with Examples
How to find dy/dx when y isn’t isolated. A 4-step implicit differentiation method with circle, x³+y³=6xy and trig examples, plus tangent lines.
Tag: chain rule
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Chain Rule Explained: Formula, Steps and 8 Examples
The chain rule differentiates composite functions: d/dx f(g(x)) = f'(g(x))·g'(x). Clear steps, 8 worked examples and the most common mistakes.
Derivative of cos²(x): −sin(2x) with Two Methods
The derivative of cos²(x) is −2sin(x)cos(x) = −sin(2x). Two methods, plus sin²(x), cos(x²) and cos²(3x) worked examples.
Derivative of e^(2x): 2e^(2x) Step by Step
The derivative of e^(2x) is 2e^(2x). Learn why with the chain rule, plus e^(kx), e^(x²), e^(−x) and x·e^(2x) examples.
Derivative of ln(x): Formula, Proof and Examples
The derivative of ln(x) is 1/x. See two short proofs, the chain rule version for ln(g(x)), worked examples and common mistakes.