Tool finds derivatives of implicit functions treating y as x or x as y. Calculator provides step-by-step explanations of the process. Users input function, differentiation variable, and optional evaluation point
Related Rates combine word problems with Implicit Differentiation. Derivative of $y=f(x)$ is $dy/dx=f'(x)=y'$. Derivative of $x=f(t)$ and $y=g(t)$ is $dx/dt=f'(t)=g'(t)$
Derivative of e^x is e^x, where e is the base. e^x has a remarkable property: its derivative is constant times itself. e approximately equals 2.718
Logarithmic differentiation involves taking logarithms first and then differentiating. Used when differentiating logarithm is easier than function itself. Efficiently calculates derivatives of power, rational and some irrational functions
Differentiation is used for finding slopes, solving optimization problems and modeling systems. First derivative is denoted by Leibniz's symbol, second derivative by Lagrange's. Derivative at a point specifies slope of function at that point
Implicit function is written in terms of both dependent and independent variables. Explicit function is represented only in terms of independent variable. Unit circle can be specified implicitly as x² + y² = 1