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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.
$\frac{d}{dx}\left(\left(8x\right)^{\left(\ln\left(8\right)+\ln\left(x\right)\right)}\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx((8x)^ln(8x)). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). To derive the function \left(8x\right)^{\left(\ln\left(8\right)+\ln\left(x\right)\right)}, use the method of logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation. Apply natural logarithm to both sides of the equality. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).