Home/Differential Calculus/Related rates/Typical examplesSection 14.2Typical examplesFormulaCopy LaTeXx2+y2=r2⇒2xdxdt+2ydydt=0x^2+y^2=r^2 \Rightarrow 2x\frac{dx}{dt}+2y\frac{dy}{dt}=0x2+y2=r2⇒2xdtdx+2ydtdy=0Related rate on a circle (constant radius).View detail →FormulavizCopy LaTeXV=43πr3⇒dVdt=4πr2drdtV=\frac{4}{3}\pi r^3 \Rightarrow \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}V=34πr3⇒dtdV=4πr2dtdrExpanding sphere.View detail →FormulaCopy LaTeXz2=x2+y2⇒2zdzdt=2xdxdt+2ydydtz^2=x^2+y^2 \Rightarrow 2z\frac{dz}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}z2=x2+y2⇒2zdtdz=2xdtdx+2ydtdyDistance in the plane.View detail →
FormulaCopy LaTeXx2+y2=r2⇒2xdxdt+2ydydt=0x^2+y^2=r^2 \Rightarrow 2x\frac{dx}{dt}+2y\frac{dy}{dt}=0x2+y2=r2⇒2xdtdx+2ydtdy=0Related rate on a circle (constant radius).View detail →
FormulavizCopy LaTeXV=43πr3⇒dVdt=4πr2drdtV=\frac{4}{3}\pi r^3 \Rightarrow \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}V=34πr3⇒dtdV=4πr2dtdrExpanding sphere.View detail →
FormulaCopy LaTeXz2=x2+y2⇒2zdzdt=2xdxdt+2ydydtz^2=x^2+y^2 \Rightarrow 2z\frac{dz}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}z2=x2+y2⇒2zdtdz=2xdtdx+2ydtdyDistance in the plane.View detail →