Question

Differentiate the equation x^4+5xy^2=10 with respect to the variable t and express [dy/dt] in terms of [dx/dt]. (Use D for [dx/dt]). The variable "t" stuff confuses me greatly.

Answer 1

\[[x(t)]^4+5x(t)[y(t)]^2=10\]
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\[[x(t)]^4=4[x(t)]^{4-1}x'(t)\]
\[[5x(t)(y(t))^2]'=5[x(t)(y(t))^2]'=5[x'(t)(y(t))^2+x(t) \cdot 2(y(t))^{2-1}y'(t)]\]
\[[10]'=0\]