What is the derivative of x^a
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Common FunctionsFunction
Derivative
Constantc0Linex1 axaSquarex22xSquare Root√x(½)x-½Exponentialexex axln(a) axLogarithmsln(x)1/x loga(x)1 / (x ln(a))Trigonometry (x is in radians)sin(x)cos(x) cos(x)−sin(x) tan(x)sec2(x)Inverse Trigonometrysin-1(x)1/√(1−x2) cos-1(x)−1/√(1−x2) tan-1(x)1/(1+x2) RulesFunction
Derivative
Multiplication by constantcfcf’Power Rulexnnxn−1Sum Rulef + gf’ + g’Difference Rulef - gf’ − g’Product Rulefgf g’ + f’ gQuotient Rulef/g(f’ g − g’ f )/g2Reciprocal Rule1/f−f’/f2 Chain Rule
(as "Composition of Functions")f º g(f’ º g) × g’Chain Rule (using ’ )f(g(x))f’(g(x))g’(x)Chain Rule (using ddx )dydx = dydududx
got from web
Derivative
Constantc0Linex1 axaSquarex22xSquare Root√x(½)x-½Exponentialexex axln(a) axLogarithmsln(x)1/x loga(x)1 / (x ln(a))Trigonometry (x is in radians)sin(x)cos(x) cos(x)−sin(x) tan(x)sec2(x)Inverse Trigonometrysin-1(x)1/√(1−x2) cos-1(x)−1/√(1−x2) tan-1(x)1/(1+x2) RulesFunction
Derivative
Multiplication by constantcfcf’Power Rulexnnxn−1Sum Rulef + gf’ + g’Difference Rulef - gf’ − g’Product Rulefgf g’ + f’ gQuotient Rulef/g(f’ g − g’ f )/g2Reciprocal Rule1/f−f’/f2 Chain Rule
(as "Composition of Functions")f º g(f’ º g) × g’Chain Rule (using ’ )f(g(x))f’(g(x))g’(x)Chain Rule (using ddx )dydx = dydududx
got from web
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