d/dx of logx
1 / x
To find the derivative of the function f(x) = log(x), where log denotes the natural logarithm, we can use the differentiation rules.
Step 1: Write the function as f(x) = ln(x), where ln represents the natural logarithm.
Step 2: Apply the power rule of differentiation. The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1). In this case, n = 1, so we have:
f'(x) = (1) * x^(1-1) = x^0 = 1
Step 3: Substitute back ln(x) for f(x):
f'(x) = 1
Therefore, the derivative of f(x) = log(x) with respect to x, d/dx(log(x)), is 1.
To find the derivative of ln(x) or log base e of x, you can use the derivative rules.
Step 1: Write the given function: ln(x) or log base e of x.
Step 2: Apply the logarithmic differentiation rule, which states that the derivative of ln(u) with respect to x is du/dx divided by u. In this case, u = x.
Step 3: Find the derivative of u with respect to x. Since u = x, du/dx is 1.
Step 4: Divide du/dx by u. In this case, we have 1/x.
Therefore, the derivative of ln(x) or log base e of x is 1/x.