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Calculus · DER

Derivative from the Limit Definition

f'(x) = lim_{h→0} [f(x+h) − f(x)] / h. For polynomials this produces the power rule.

CalculusCommon Core CHA-2.BDERVerified correct ✓

Worked examples

Find d/dx[-4*x**4 - 5*x**3 + x**2 - 4*x - 1].
Answer: -16*x**3 - 15*x**2 + 2*x - 4
Find d/dx[-x**4 + 4*x**3 - 4*x**2 + 2*x - 2].
Answer: -4*x**3 + 12*x**2 - 8*x + 2

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Evaluate Limits Algebraically — Substitution and Factoring

More Calculus topics

Evaluate Limits Algebraically — Substitution and FactoringEvaluate Trigonometric Limits — sin(x)/x as x→0Limits at Infinity — End Behavior of Rational FunctionsTest Continuity at a Point — Three-Part DefinitionPower Rule — Differentiate Polynomial FunctionsProduct Rule — Differentiate a Product of Two FunctionsChain Rule — Differentiate Composite FunctionsDerivatives of Trig Functions — sin, cos, tan