If y=x^3 x, then find d^4 y d x^4 . - Vidyadip

Question

If $y=x^3 \log x$, then find $\frac{d^4 y}{d x^4}$.

✓

Answer

If
$y=x^3 \log x$
$\therefore \quad \frac{d y}{d x}=\frac{d}{d x}\left(x^3 \log x\right)$
$\frac{d y}{d x}=x^2(1+3 \log x)$
$\frac{d^2 y}{d x^2}=x^2 \frac{d}{d x}(1+3 \log x)+(1+3 \log x) \frac{d}{d x} x^2$
$\frac{d^2 y}{d x^2}=x(5+6 \log x)$
$\frac{d^3 y}{d x^3}=x \frac{d}{d x}(5+6 \log x)+(5+6 \log x) \frac{d}{d x} x$
$\frac{d^3 y}{d x^3}=11+6 \log x$
$\frac{d^4 y}{d x^4}=\frac{6}{x}$

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