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Step-by-step Solution
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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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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^x$ and $g=\log_{2}\left(x^4-1\right)$
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$\frac{d}{dx}\left(x^x\right)\log_{2}\left(x^4-1\right)+x^x\frac{d}{dx}\left(\log_{2}\left(x^4-1\right)\right)$
Learn how to solve problems step by step online. Find the derivative of x^xlog2(x^4+-1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^x and g=\log_{2}\left(x^4-1\right). We can find the derivative of a logarithm of any base using the change of base formula. Before deriving, we must pass the logarithm to base e: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. The derivative of a function multiplied by a constant (\frac{1}{\ln\left(2\right)}) is equal to the constant times the derivative of the function. 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}.
