Final answer to the problem
$\frac{-2}{3\sqrt[3]{x^{5}}}$
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Step-by-step Solution
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- Find the derivative
- 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
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
$-\frac{2}{3}x^{\left(-\frac{2}{3}-1\right)}$
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$-\frac{2}{3}x^{\left(-\frac{2}{3}-1\right)}$
Learn how to solve problems step by step online. Find the derivative d/dx(x^(-2/3)) using the power rule. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiplying fractions -\frac{2}{3} \times \frac{1}{x^{\left|-\frac{5}{3}\right|}}. Multiplying fractions -\frac{2}{3} \times \frac{1}{\sqrt[3]{x^{5}}}.
Final answer to the problem
$\frac{-2}{3\sqrt[3]{x^{5}}}$
