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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{x^{\frac{3}{x}}}\frac{d}{dx}\left(x^{\frac{3}{x}}\right)$
Learn how to solve problems step by step online. Find the derivative of ln(x^(3/x)). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative \frac{d}{dx}\left(x^{\frac{3}{x}}\right) results in 3\left(1-\ln\left(x\right)\right)x^{\left(\frac{3}{x}-2\right)}. Multiplying the fraction by 3\left(1-\ln\left(x\right)\right)x^{\left(\frac{3}{x}-2\right)}. Simplify the fraction \frac{3\left(1-\ln\left(x\right)\right)x^{\left(\frac{3}{x}-2\right)}}{x^{\frac{3}{x}}} by x.
