Local Linear Approximation; Differentials Solutions To Selected ...
Local Linear Approximation; Differentials Solutions To Selected ...
Local Linear Approximation; Differentials Solutions To Selected ...
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(d) y = x √ 1 − x = x(1 − x) 1/2<br />
(e)<br />
dy = d(x(1 − x) 1/2 )<br />
= x d(1 − x) 1/2 + (1 − x) 1/2 dx<br />
�<br />
1<br />
= x<br />
2 (1 − x)−1/2 �<br />
(−1)dx + (1 − x) 1/2 dx<br />
x<br />
= −<br />
2 √ 1 − x dx + √ 1 − x dx<br />
�<br />
√1 x<br />
= − x −<br />
2 √ �<br />
dx<br />
1 − x<br />
�<br />
√1 2<br />
= − x · √ 1 − x<br />
2 √ 1 − x −<br />
x<br />
2 √ �<br />
dx<br />
1 − x<br />
�<br />
2(1 − x) − x<br />
=<br />
2 √ �<br />
dx<br />
x<br />
�<br />
2 − 3x<br />
=<br />
2 √ �<br />
dx<br />
1 − x<br />
y = (1 + x) −17<br />
dy = d(1 + x) −17<br />
= −17(1 + x) −18 dx<br />
= − 17<br />
dx<br />
(1 + x) 18<br />
7
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