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The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dt}\left(\ln\left(\sqrt{t+2}\right)-\ln\left(t^2\cos\left(t\right)\right)\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dt(ln(((t+2)^1/2)/(t^2cos(t)))). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Simplify the product -(\ln\left(t^2\right)+\ln\left(\cos\left(t\right)\right)).