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Higher Order Monomial Derivative Calculator

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Higher Order Monomial Derivative Calculator

For f(x)=a·x^m with real a and integer m≥0, the k-th derivative at x0 is 0 if k>m; else a·m!/(m−k)!·x0^(m−k).

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What is Higher Order Monomial Derivative Calculator?

Computes the nth derivative of monomials using repeated power-rule application.

Higher Order Monomial Derivative Calculator Formula / Method

dn/dxn(axk)=a×k!/(k−n)!×x(k−n),forn≤kd^n/dx^n(ax^k) = a × k!/(k−n)! × x^(k−n), for n ≤ k
dn/dxn(axk)=0,forn>kd^n/dx^n(ax^k) = 0, for n > k

Higher Order Monomial Derivative Calculator Worked Example

Forf(x)=5x7,thirdderivative:For f(x)=5x^7, third derivative:
f′(x)=35x6f'(x)=35x^6
f′′(x)=210x5f''(x)=210x^5
f′′′(x)=1050x4f'''(x)=1050x^4
Direct:d3/dx3(5x7)=5×7!/4!×x4=1050x4Direct: d^3/dx^3(5x^7)=5×7!/4!×x^4=1050x^4

Where Higher Order Monomial Derivative Calculator Is Applied

  • Calculus coursework
  • Taylor/Maclaurin series
  • Physics motion derivatives
  • CAS validation

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