The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

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 ($\frac{1}{\ln\left(10\right)}$) 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 $\displaystyle f'(x)=\frac{a'}{a}$