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
Use the definition of ##e## as the unique positive number for which ##\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) = e^x## is equal to ##e^x##
Determine the derivative of ##f(x) = 2x^5 - 3e^{6x}##
Find the derivative of ##f(x) = x^{3}e^{-2x}##
Determine the slope of the tangent line to the function ##f(x) = 2e^{-3x}##at ##(0,2)##
For the following problem, find the derivative of ##f(x) = 5^{x^{3} - 4}##
Use logarithmic differentiation to find the derivative in the following example
##g(x) = \log_{3}(2x^{2} - 5x)##
##g(x) = \log_{3}(2x^{2} - 5x)##
Find the derivative of ##h(x) = 8^{x}\log_{9}x##
Use the properties of logarithms to show that the derivative of ##\log_{a}x = \frac{1}{(\ln{a})x}##
Use implicit differentiation to show that the derivative of ##\ln{x} = \frac{1}{x}## for ##x > 0##
Note that many classes introduce logarithmic differentiation before implicit differentiation.
Note that many classes introduce logarithmic differentiation before implicit differentiation.
Differentiate ##f(x) = \ln{6x^2}##
Find the derivative of ##f(x) = \frac{\ln{(2x)}}{x^4}##