Apply constant multiple rule: Apply the constant multiple rule to the logarithmic functions. The derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. Therefore, we can take the constants out of the derivative. f'(x) = 3 * d/dx(log(x)) + 3 * d/dx(log(3))Recognize derivative of constant: Recognize that the derivative of a constant is zero. The function log(3) is a constant because it does not depend on x. Therefore, its derivative is zero. f'(x) = 3 * d/dx(log(x)) + 0Calculate derivative of log(x): Calculate the derivative of log(x) with respect to x. The derivative of log(x) with respect to x is 1/x. f'(x) = 3 * (1/x)Simplify expression: Simplify the expression. Now we can simplify the expression by multiplying the constant 3 by the derivative of log(x). f'(x) = 3/x

Calculus

Find derivatives of logarithmic functions

Full solution

3\log(x)+3\log(3)

Apply constant multiple rule: Apply the constant multiple rule to the logarithmic functions. $\newline$ The derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. Therefore, we can take the constants out of the derivative. $\newline$ $f'(x) = 3 \cdot \frac{d}{dx}(\log(x)) + 3 \cdot \frac{d}{dx}(\log(3))$
Recognize derivative of constant: Recognize that the derivative of a constant is $0$ . The function $\log(3)$ is a constant because it does not depend on $x$ . Therefore, its derivative is $0$ . $f'(x) = 3 \cdot \frac{d}{dx}(\log(x)) + 0$
Calculate derivative of log(x): Calculate the derivative of $\log(x)$ with respect to $x$ . The derivative of $\log(x)$ with respect to $x$ is $\frac{1}{x}$ . $f'(x) = 3 \cdot \left(\frac{1}{x}\right)$
Simplify expression: Simplify the expression. $\newline$ Now we can simplify the expression by multiplying the constant $3$ by the derivative of $\log(x)$ . $\newline$ $f'(x) = \frac{3}{x}$