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Apply the formula: $\frac{d}{dx}\left(\frac{a}{b}\right)$$=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$, where $a=\ln\left(x\right)$ and $b=x^3$
Learn how to solve règle du quotient de la différentiation problems step by step online.
$\frac{\frac{d}{dx}\left(\ln\left(x\right)\right)x^3-\frac{d}{dx}\left(x^3\right)\ln\left(x\right)}{\left(x^3\right)^2}$
Learn how to solve règle du quotient de la différentiation problems step by step online. Find the derivative d/dx(ln(x)/(x^3)). Apply the formula: \frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}, where a=\ln\left(x\right) and b=x^3. Simplify \left(x^3\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 2. Apply the formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}. Apply the formula: ab=ab, where ab=- 3x^{2}\ln\left(x\right), a=-1 and b=3.
