Final answer to the problem
Step-by-step Solution
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- 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 $f=x^4$ and $g=\log_{5}\left(x\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(x^4\right)\log_{5}\left(x\right)+x^4\frac{d}{dx}\left(\log_{5}\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of x^4log5(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^4 and g=\log_{5}\left(x\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. 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(5\right)}) is equal to the constant times the derivative of the function.
