Final answer to the problem
$\frac{1}{\ln\left(2\right)x}$
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Step-by-step Solution
Learn how to solve integral calculus problems step by step online. Find the derivative of log2(5*x). We can find the derivative of a logarithm of any base using the change of base formula. Before deriving, we must pass the logarithm to base e: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. The derivative of a function multiplied by a constant (\frac{1}{\ln\left(2\right)}) is equal to the constant times the derivative of the function. 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}. Multiplying fractions \frac{1}{\ln\left(2\right)} \times \frac{1}{5x}.
Final answer to the problem
$\frac{1}{\ln\left(2\right)x}$
