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What is the derivative of #pi#?

1 Answer
Mar 3, 2018

Answer:

#0#; Derivative of a constant is always #0#

Explanation:

The derivative of a constant term is always zero. Reason being, we take derivatives with respect to a variable.

We understand derivatives to be the slope of the tangent line, or our instantaneous rate of change. Take the following derivative:

#d/dx[2x+8]=2#

This expression that we're taking the derivative of is in slope-intercept form (#y=mx+b#), where #m# is the slope. In our case, the slope is #2#, so the derivative is #2#.

Remember, #d/dx# means we're taking the derivative with respect to #x#, or how much #y# changes with respect to #x#. #pi# is just a constant, meaning it doesn't change with respect to a variable . It will graph as a horizontal line, just like #2, 8,#and #11# will. As we know, slopes of horizontal lines are #0#, so the derivative of a constant, like #pi#, will always be zero.