Final answer to the problem
$e^x\left(2x^{2x}\ln\left(x\right)+3x^{2x}\right)$
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Step-by-step Solution
How should I solve this problem?
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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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1
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^{2x}$ and $g=e^x$
Learn how to solve rational equations problems step by step online.
$\frac{d}{dx}\left(x^{2x}\right)e^x+x^{2x}\frac{d}{dx}\left(e^x\right)$
Learn how to solve rational equations problems step by step online. Find the derivative of x^(2x)e^x. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^{2x} and g=e^x. Applying the derivative of the exponential function. The derivative \frac{d}{dx}\left(x^{2x}\right) results in 2\left(\ln\left(x\right)+1\right)x^{2x}. Simplify the derivative.
Final answer to the problem
$e^x\left(2x^{2x}\ln\left(x\right)+3x^{2x}\right)$
