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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.
$\frac{d}{dx}\left(\frac{1}{2}\left(x^3+4\right)^6\ln\left(5x+1\right)\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln((5x+1)^1/2)(x^3+4)^6). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The derivative of a function multiplied by a constant 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=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.