Final answer to the problem
$\left(\ln\left(x\right)+1\right)x^x3^x+\ln\left(3\right)x^x3^x$
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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 $f=x^x$ and $g=3^x$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(x^x\right)3^x+x^x\frac{d}{dx}\left(3^x\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of x^x3^x. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^x and g=3^x. Applying the derivative of the exponential function. The derivative of the linear function is equal to 1. The derivative \frac{d}{dx}\left(x^x\right) results in \left(\ln\left(x\right)+1\right)x^x.
Final answer to the problem
$\left(\ln\left(x\right)+1\right)x^x3^x+\ln\left(3\right)x^x3^x$
