Explore the concept of logarithmic derivatives in calculus through a comprehensive 90-minute tutorial. Delve into various problem-solving techniques using examples from James Stewart's single variable calculus textbook. Learn to differentiate complex logarithmic expressions, including natural logarithms and logarithms with different bases. Practice finding derivatives of functions involving logarithms combined with algebraic, trigonometric, and exponential elements. Master the application of logarithmic differentiation to simplify complex derivative calculations. Tackle second derivatives, tangent line equations, and compare regular derivative methods with logarithmic approaches. Enhance your calculus skills by working through a diverse set of challenging problems that demonstrate the power and versatility of logarithmic derivatives.
Overview
Syllabus
Derivative of ln(1/x).
derivative of log base 10 of (x^3+1), with the box.
derivative of ln(x*sqrt(x^2-1)) vs. derivative of ln(x+sqrt(x^2-1)).
derivative of ln((2y+1)^5/sqrt(y^2+1)).
derivative of ln(ln(s)).
Derivative of ln(e^-x + x*e^-x).
derivative of 2x*log_10(sqrt(x)).
second derivative of x^2*ln(2x).
second derivative of ln(x+sqrt(1+x^2)).
equation of the line tangent to ln(x^2-3x+1) at x=3.
derivative of sqrt((x-1)/(x^4+1)), logarithmic differentiation.
derivative of x^sin(x),.
derivative of x^x.
regular derivative vs. logarithmic derivative.
derivative of 1/ln(x).
derivative of ln(1/x).
logarithmic differentation.
Taught by
blackpenredpen
