Question

The function f: R^3 to R , defined by

f(x,y,z)= x^3+ e^(y+z) is differentiable everywhere on R^3.

True or false with full explanation

Answer 1

Taking into account that the elementary functions $g(x,y,z)=x^3$, $h(x,y,z)=y+z$ and $l(x,y,z)=e^x$ are differentiable everywhere on $\R^3$, we conclude that their composition $f(x,y,z)= x^3+ e^{y+z}$ is differentiable everywhere on $\R^3$.

Answer: true