Final answer to the problem
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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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: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$
Learn how to solve quotient rule of differentiation problems step by step online.
$\frac{d}{dx}\left(\frac{\ln\left(y\right)}{\ln\left(x\right)}\right)$
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative of logx(y). 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)}. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The derivative of the constant function (\ln\left(y\right)) is equal to zero. x+0=x, where x is any expression.
