Question

help please:
If f(x,y) = x²+xy²-y³ and x=t²+3 and y=t³+5t , then find
δf/δx
δf/δt

Answer 1

\[\frac{∂f}{∂x}=\frac{∂}{∂x}(x^2+xy^2-y^2)\]Just treat the y's retriceconstants.

For the second one you need to use the chain rule for functions of multiple variables.
\[\frac{∂f}{∂t}=\frac{∂f}{∂x} \frac{∂x}{∂t}+\frac{∂f}{∂y}\frac{∂y}{∂t}=f_xx_t+f_yy_t\]