Given , derive an explicit expression for valid for every integer . Express your…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Given

f(x)=2x^{4}-6x^{3}+3x^{2}-x+7

, derive an explicit expression for

f^{(n)}(x)

valid for every integer

n\ge 0

. Express your answer in closed form using factorial notation and indicate any values of

n

for which the expression is zero.

Related theory

Higher-Order Derivatives
Advanced Differentiation
Differentiation Rules
Second order derivatives
Continuity and Differentiability

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