Calculus 1: Implicit Differentiation
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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 implicit differentiation to find ##\frac{dy}{dx}## for the following equation
##x^2 + y^2 = 25 + 5x##
##x^2 + y^2 = 25 + 5x##
For the following function, find ##\frac{dy}{dx}## by implicit differentiation
##x^2 + 2xy + y^2 = 5##
##x^2 + 2xy + y^2 = 5##
Use implicit differentiation to take the derivative of ##y## with respect to ##x## for the following equation
##y^5 + 2y = x^2##
##y^5 + 2y = x^2##
Find ##\frac{dy}{dx}## when ##x^3 + 3y^4 = 2x + 7##
Find the derivative of ##y## with respect to ##x## for the following equation
##y(x+4) = x^2 - 3##
##y(x+4) = x^2 - 3##
Find ##\frac{dy}{dx}## for ##x^2 + y^3 = \log{(x + y)}##
For the following equation, differentiate implicitly to find ##\frac{dy}{dx}##
##e^{(x + y)} = \sin{(x)} + \cos{(y)}##
##e^{(x + y)} = \sin{(x)} + \cos{(y)}##
Find the tangent line to the curve ##xy + \ln{(xy^2)} = 1## at the point ##(1,1)##
Find ##\frac{dy}{dx}## and the slope of the tangent line at ##(-2, 1)## for the curve given by
##2x^2 - 3y^3 = 5##
##2x^2 - 3y^3 = 5##
Find ##\frac{dy}{dx}## and the slope of the tangent line at (0,3) for the curve given by
##y^3 + x^{2}y^{5} - x^4 = 27##
##y^3 + x^{2}y^{5} - x^4 = 27##
Determine the first and second derivatives, ##\frac{dy}{dx}## and ##\frac{d^{2}y}{dx^2}## for the following equation
##x^2 + xy = 4##
##x^2 + xy = 4##