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Calculate each of the following derivatives using only the definition of the derivative. (a) f(x) = x³, f'(2); (b) g(x)=x+2, g'(a) (for arbitrary a € R); (c) h(x) = x² cos(x), g'(0); (d) r(x) = 32±4, h'(1). 2x-1'

Calculate each of the following derivatives using only the definition of the derivative. (a) f(x) = x³, f'(2); (b) g(x)=x+2, g'(a) (for arbitrary a € R); (c) h(x) = x² cos(x), g'(0); (d) r(x) = 32±4, h'(1). 2x-1'

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Calculate each of the following derivatives using only the definition of the derivative. (a) \( f(x) = x^3 \), \( f'(2) \); (b) \( g(x) = x + 2 \), \( g'(a) \) (for arbitrary \( a \in \mathbb{R} \)); (c) \( h(x) = x^2 \cos(x) \), \( g'(0) \); (d) \( r(x) = \frac{3x+4}{2x-1} \), \( h'(1) \).
Transcribed Image Text:Calculate each of the following derivatives using only the definition of the derivative. (a) \( f(x) = x^3 \), \( f'(2) \); (b) \( g(x) = x + 2 \), \( g'(a) \) (for arbitrary \( a \in \mathbb{R} \)); (c) \( h(x) = x^2 \cos(x) \), \( g'(0) \); (d) \( r(x) = \frac{3x+4}{2x-1} \), \( h'(1) \).
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