GUIDE深度 · Deep dive
Derivative Rules
Power rule: d/dx x^n = n x^(n-1); constants differentiate to 0; sums/differences differentiate term by term. A second derivative is two derivatives in a row. Split the polynomial into terms first.
Rules
x^4 -> 4x^3.
3x^2 -> 6x.
constant 5 -> 0.
Second
Find f'(x), then differentiate f'(x).
f''(x) describes concavity/acceleration.
Write each term on its own line before differentiating; this keeps coefficients and exponents from getting mixed up.
FAQ
What about coefficients?
Keep the coefficient; differentiate the power.
Derivative of x?
1.