# Calculus 1: Logarithmic 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

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For the following function, use logarithmic differentiation to find $\frac{dy}{dx}$

$y = \frac{{(x + 2)}^2}{\sqrt{x^2 + 1}}$

Find the derivative of the following function $y = x^{\frac{2}{x}}$

Find the derivative of the following function

$y = \sqrt{(x^2 + 1){(x - 1)}^2}$

Determine $\frac{dy}{dx}$ for the following function

$y = \sqrt{\frac{1}{x (x + 1)}}$

Use logarithmic differentiation to find the first derivative of the function

$y = x^{x + 1}$

Find the derivative of $y = x^{\sin{(x)}}$

Find the derivative of ${(\ln{x})}^{(\ln{(x)})}$

Use logarithmic differentiation to find the derivative of the following function

$y = \frac{(x - 1)(x + 2)(x + 3)(x - 4)}{(x + 5)(x - 3)}$