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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dx}\left(36x^4\ln\left(x\right)+\ln\left(x\right)^5\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(9x^4ln(x^4)+ln(x)^5). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (36) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^4 and g=\ln\left(x\right).