Calculus 1: Inverse and Hyperbolic Trig Derivatives
Expand
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
Find the derivative, ##y^{\prime}## of the following implicit function
##y = \tan^{-1}(xy)##
##y = \tan^{-1}(xy)##
Show that ##\frac{d}{dx}(\arcsin{x}) = \frac{x^{\prime}}{\sqrt{1 - x^2}}##
Determine the derivative of the following inverse trig function
##f(x) = \arctan{(\sqrt{x})}##
##f(x) = \arctan{(\sqrt{x})}##
Determine the derivative of the inverse trigonometric function
##f(x) = \sec^{-1}{(5x)}##
##f(x) = \sec^{-1}{(5x)}##
Find the derivative of ##f(x) = 2\arccos{(\frac{x}{3})}##
Determine the derivative of ##f(t) = \sin{(\arccos{(t)})}##
Let ##f(x) = \tan{(x)}## on the interval ##\frac{-\pi}{2}## < ##x## < ##\frac{\pi}{2}##
What is ##\frac{d}{dx}(\arctan{(x)})## ?
What is ##\frac{d}{dx}(\arctan{(x)})## ?
Show that for ##y = \cos^{-1}(x)## the first derivative, ##\frac{dy}{dx} = \frac{1}{x^2 + 1}##
For the following function, find the first derivative
##\theta = \frac{\tan^{-1}(2r)}{\pi{r}}##
##\theta = \frac{\tan^{-1}(2r)}{\pi{r}}##
Find the derivative of the following hyperbolic function
##f(x) = \sin{(\sinh{(x)})}##
##f(x) = \sin{(\sinh{(x)})}##
Find the derivative of ##f(x) = {(\sinh^{-1}(x))}^{\frac{3}{2}}##
Find the derivative of ##\sinh{(x)}## and ##\cosh{(x)}##
Find the derivative of ##\tanh{(3^{x^2} + 4x)}##