A student attempts to differentiate the function x x using the power rule, mistakenly getting x ⋅ x x − 1 . A second student attempts to differentiate x x by treating it as an exponential function, mistakenly getting ln x x x . Use the chain rule to explain why the correct derivative is the sum of these two incorrect results.
A student attempts to differentiate the function x x using the power rule, mistakenly getting x ⋅ x x − 1 . A second student attempts to differentiate x x by treating it as an exponential function, mistakenly getting ln x x x . Use the chain rule to explain why the correct derivative is the sum of these two incorrect results.
A student attempts to differentiate the function
x
x
using the power rule, mistakenly getting
x
⋅
x
x
−
1
.
A second student attempts to differentiate
x
x
by treating it as an exponential function, mistakenly getting
ln
x
x
x
.
Use the chain rule to explain why the correct derivative is the sum of these two incorrect results.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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