multivariable Derivative

[lldk]

I try to find out dx/dt ,dy/dt and dz/dt, first, but is it worng? Because I don’t know what is the next after I find out dx/dt ,dy/dt and dz/dt

 

[Romsek]

[MATH]\left . \dfrac{dw}{dt}\right|_{(x,y,z)=(1,\ln(2),0)} = \left . \dfrac{dw}{dx}\dfrac{dx}{dt} +\dfrac{dw}{dy}\dfrac{dy}{dt} +\dfrac{dw}{dz}\dfrac{dz}{dt} \right|_{t=0}[/MATH]

 

[lldk]

[MATH]\left . \dfrac{dw}{dt}\right|_{(x,y,z)=(1,\ln(2),0)} = \left . \dfrac{dw}{dx}\dfrac{dx}{dt} +\dfrac{dw}{dy}\dfrac{dy}{dt} +\dfrac{dw}{dz}\dfrac{dz}{dt} \right|_{t=0}[/MATH]

May I ask why t=0？

 

[Romsek]

May I ask why t=0？

compare [MATH](1,\ln(2),0)[/MATH] with [MATH](\cos(t), \ln(t+2), t)[/MATH]

 

[lldk]

compare [MATH](1,\ln(2),0)[/MATH] with [MATH](\cos(t), \ln(t+2), t)[/MATH]

I get it， thx