# Derivation Question

• Jan 20th 2010, 10:17 PM
Sprintz
Derivation Question
Two Questions for the community:

1) Let s(x) = x^(1/4), where x(t) = ln(f(t)) and f(t) is a differentiable function. Find ds/dt.

2) Consider the function f(x0 = x^2 * e^(-x)

Find the best linear approximation to f at x = 0, and compute the 2nd order Taylor polynomial at x = 0.

I'm having problems with this question (I'm in Calc III and this is part of a long review sheet from Calc II; any help would be much appreciated)

Cheers
• Jan 20th 2010, 10:38 PM
Prove It
Quote:

Originally Posted by Sprintz
Two Questions for the community:

1) Let s(x) = x^(1/4), where x(t) = ln(f(t)) and f(t) is a differentiable function. Find ds/dt.

2) Consider the function f(x0 = x^2 * e^(-x)

Find the best linear approximation to f at x = 0, and compute the 2nd order Taylor polynomial at x = 0.

I'm having problems with this question (I'm in Calc III and this is part of a long review sheet from Calc II; any help would be much appreciated)

Cheers

1. Use the chain rule.

$\displaystyle \frac{ds}{dt} = \frac{ds}{dx}\,\frac{dx}{dt}$.