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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 differential calculus problems step by step online.
$\frac{d}{dx}\left(\frac{\ln\left(x\right)}{\ln\left(a\right)}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of loga(x). 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(a\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}. Multiplying fractions \frac{1}{\ln\left(a\right)} \times \frac{1}{x}.
