(a) Write | x | = x 2 and use the Chain Rule to show that (b) If f ( x ) = | s i n x | , find f′(x) and sketch the graphs of f and f′ . Where is f not differentiable ? (c) If g ( x ) = s i n | x | , find g'(x) and sketch the graphs of g and g'. Where is g not differentiable?
Solution Summary: The author explains how to use the chain rule to show that x is non-zero.
(a) Write
|
x
|
=
x
2
and use the Chain Rule to show that
(b) If
f
(
x
)
=
|
s
i
n
x
|
, find f′(x) and sketch the graphs of f and f′. Where is f not differentiable?
(c) If
g
(
x
)
=
s
i
n
|
x
|
, find g'(x) and sketch the graphs of g and g'. Where is g not differentiable?
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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