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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dx}\left(\sqrt{xy}+\sqrt{x}-\left(\ln\left(x\right)+\ln\left(y\right)\right)\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx((xy)^1/2+x^1/2-ln(xy)). 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(x\right)+\ln\left(y\right)). The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (-\ln\left(y\right)) is equal to zero.