Learn implicit differentiation techniques and how to find derivatives of inverse trigonometric functions in this 30-minute calculus video. Explore various examples, including complex equations involving trigonometric and exponential functions, and practice finding first and second derivatives using implicit differentiation. Master the application of the chain rule to solve problems with inverse trig functions, and compare different approaches to similar problems. Gain a deeper understanding of calculus concepts through step-by-step explanations of challenging problems, such as finding the derivative of a cardioid at a specific point.
Implicit Differentiation & Derivative of Inverse Trig Functions - Calculus
Overview
Syllabus
implicit differentiation y*cos(x)=x^2+y^2.
derivative for e^(x/y) = x - y.
implicit differentiation 4cos(x)sin(y)=1.
implicit differentiation arctan(x^2*y)=x+x*y^2.
Second derivative with implicit differentiation 9x^2+y^2=9.
Derivative of (arctan(x))^2.
derivative of sin^-1(2x+1).
y'' for sin(y)+cos(x)=1, implicit differentiation.
derivative of sin(x*y)=cos(x+y), implicit differentiation.
dy/dx of a cardioid at (0, 1/2), implicit differentiation.
Derivative of cos(sin^-1(x)).
derivative of sin^-1(2x+1).
derivative of sqrt(1-x^2)*arccos(x).
derivative of (tan^-1(x))^2 vs derivative of tan^-1(x^2).
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