Ҳосилаи функсияи \(y = \ln(3x^4+6)\) ёфта шавад.

Ҳал.

\(\begin{multline}
y' = (\ln(3x^4+6))' = \frac{1}{3x^4+6}\cdot (3x^4+6)' = \frac{1}{3x^4+6}\cdot (3\cdot 4 \cdot x^3) = \\
= \frac{3 \cdot 4 \cdot x^3}{3 \cdot (x^4+2)} = \frac{4 \cdot x^3}{x^4+2}.
\end{multline}\)

Ҷавоб.

\[y' = \frac{4x^3}{x^4+2}.\]