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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{dx}\left(x^6\right)+\frac{d}{dx}\left(\frac{-6}{x^5}\right)+\frac{d}{dx}\left(e^{-4x}\right)+\frac{d}{dx}\left(\ln\left(3x\right)\right)+\frac{d}{dx}\left(\frac{-5}{x}\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method f(x)=x^6+-6/(x^5)e^(-4x)ln(3x)-5/x. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the derivative of the exponential function.