Suppose f is continuous on [a, b], ƒ'(x) exists at some point x e [a, b], g is defined on an interval I which contains the range of f and g is differentiable at the point f (x). If h(t) = g (f (t)) (a < t < b), then show that h is differentiable at x, and h'(x) = g '(f(x)). f'(x).
Suppose f is continuous on [a, b], ƒ'(x) exists at some point x e [a, b], g is defined on an interval I which contains the range of f and g is differentiable at the point f (x). If h(t) = g (f (t)) (a < t < b), then show that h is differentiable at x, and h'(x) = g '(f(x)). f'(x).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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