Derivative of:ln (x)
The derivative of ln(x) can be found using the rules of calculus
The derivative of ln(x) can be found using the rules of calculus. The natural logarithm function, ln(x), represents the logarithm to the base e, where e is a mathematical constant approximately equal to 2.71828.
To find the derivative, we’ll use the differentiation rule for logarithmic functions:
d/dx [ln(x)] = 1/x
This means that the derivative of ln(x) with respect to x is equal to 1 divided by x.
To understand this, let’s go through the process of finding the derivative step by step.
Step 1: Write down the expression for the natural logarithm function:
ln(x)
Step 2: Apply the differentiation rule for logarithmic functions, which states that the derivative of ln(x) is equal to 1 divided by x:
d/dx [ln(x)] = 1/x
Step 3: Simplify the expression, if necessary.
Step 4: Since the derivative of ln(x) is always 1/x, we can conclude that the slope of the tangent line to the graph of ln(x) at any point (x, ln(x)) is 1 divided by x.
To summarize, the derivative of ln(x) with respect to x is equal to 1 divided by x.
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