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Calculus 1: Exponential and Logarithmic Functions

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All Calculus 1LimitsDefinition of the DerivativeProduct and Quotient RulePower Rule and Basic DerivativesDerivatives of Trig FunctionsExponential and Logarithmic FunctionsChain RuleInverse and Hyperbolic Trig DerivativesImplicit DifferentiationRelated Rates ProblemsLogarithmic DifferentiationGraphing and Critical PointsOptimization ProblemsIndeterminate Forms and l'Hospital's RuleLinear Approximation and DifferentialsNewton Raphson MethodIndefinite IntegralsU SubstitutionDefinite Integrals and Fundamental TheoremApplications of Integration
Derivative of Exponential

Use the definition of ee as the unique positive number for which lim⁡h→0eh−1h=1\lim_{h\rightarrow 0}\frac{e^{h} - 1}{h} = 1 and the definition of the derivative to show that derivative of the exponential function, f(x)=exf(x) = e^x is equal to exe^x

Exponential and Logarithmic FunctionsHardVideo
Derivatives of Exponential Derivatives

Determine the derivative of f(x)=2x5−3e6xf(x) = 2x^5 - 3e^{6x}

Exponential and Logarithmic FunctionsHardVideo
Log Differentiation Examples

Use logarithmic differentiation to find the derivative in the following example

g(x)=log⁡3(2x2−5x)g(x) = \log_{3}(2x^{2} - 5x)

Exponential and Logarithmic FunctionsHardVideo