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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 $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{2^{\left(3x+5\right)}}\frac{d}{dx}\left(2^{\left(3x+5\right)}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule d/dx(ln(2^(3x+5))). 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}. Applying the derivative of the exponential function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (5) is equal to zero.