Mathematics

This is the definition of a derivative—you're finding the instantaneous rate of change of $f(x) = x^4$. Rather than using the limit definition directly, expand $(x+h)^4$ using the binomial theorem, then watch how most terms vanish as $h \to 0$. The key is that only terms containing at least one factor of $h$ in the numerator will survive after dividing by $h$.

This is the definition of a derivative—you're finding the instantaneous rate of change of $f(x) = x^4$. Rather than using the limit definition directly, expand $(x+h)^4$ using the binomial theorem, then watch how most terms vanish as $h \to 0$. The key is that only terms containing at least one factor of $h$ in the numerator will survive after dividing by $h$.