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The derivative of a sum of two or more functions is the sum of the derivatives of each function
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(x^6\right)+\frac{d}{dx}\left(\frac{-6}{x^5}\right)+\frac{d}{dx}\left(e^{-4x}\right)+\frac{d}{dx}\left(\ln\left(3x\right)\right)+\frac{d}{dx}\left(\frac{-5}{x}\right)$
Learn how to solve differential calculus problems step by step online. Simplify the expression 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. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of the linear function times a constant, is equal to the constant.