Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^x$ and $g=\ln\left(x\right)^{\cos\left(2x\right)}$
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$\frac{d}{dx}\left(x^x\right)\ln\left(x\right)^{\cos\left(2x\right)}+x^x\frac{d}{dx}\left(\ln\left(x\right)^{\cos\left(2x\right)}\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative of x^xln(x)^cos(2x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^x and g=\ln\left(x\right)^{\cos\left(2x\right)}. The derivative \frac{d}{dx}\left(x^x\right) results in \left(\ln\left(x\right)+1\right)x^x. The derivative \frac{d}{dx}\left(\ln\left(x\right)^{\cos\left(2x\right)}\right) results in \left(-2\sin\left(2x\right)\ln\left(\ln\left(x\right)\right)+\frac{\cos\left(2x\right)}{x\ln\left(x\right)}\right)\ln\left(x\right)^{\cos\left(2x\right)}.
