Find

dydx

by implicit differentiation.

x$3+$ y$4=5$

Step $1$

When finding

dydx

$=$ y$$

by implicit differentiation, we consider y to be a function of x$.$ This means that whenever a derivative is calculated for an expression that includes the variable y$,$ the chain rule requires that we multiply the derivative by

y$.$

For example,

ddx

$$

y$2$

$=(2$y$)($y$).$

Similarly,

ddx

y$4$

$=$