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EXERCISES 14.4 Chain Rule: One Independent Variable In Exercises 1-6, (a) express $\frac{dw}{dt}$ as a function of $t$, both by using the Chain Rule and by expressing $w$ in terms of $t$ and differentiating directly with respect to $t$. Then (b) evaluate $\frac{dw}{dt}$ at the given value of $t$. 1. $w = x^2 + y^2$, $x = \cos t$, $y = \sin t$; $t = \pi$ 2. $w = x^2 + y^2$, $x = \cos t + \sin t$, $y = \cos t - \sin t$; $t = 0$ 3. $w = \frac{x}{z} + \frac{y}{z}$, $x = \cos^2 t$, $y = \sin^2 t$, $z = 1/t$; $t = 3$ 4. $w = \ln (x^2 + y^2 + z^2)$, $x = \cos t$, $y = \sin t$, $z = 4\sqrt{t}$; $t = 3$

          EXERCISES 14.4
Chain Rule: One Independent Variable
In Exercises 1-6, (a) express $\frac{dw}{dt}$ as a function of $t$, both by using
the Chain Rule and by expressing $w$ in terms of $t$ and differentiating
directly with respect to $t$. Then (b) evaluate $\frac{dw}{dt}$ at the given value
of $t$.
1. $w = x^2 + y^2$, $x = \cos t$, $y = \sin t$; $t = \pi$
2. $w = x^2 + y^2$, $x = \cos t + \sin t$, $y = \cos t - \sin t$; $t = 0$
3. $w = \frac{x}{z} + \frac{y}{z}$, $x = \cos^2 t$, $y = \sin^2 t$, $z = 1/t$; $t = 3$
4. $w = \ln (x^2 + y^2 + z^2)$, $x = \cos t$, $y = \sin t$, $z = 4\sqrt{t}$;
$t = 3$

EXERCISES 14.4
Chain Rule: One Independent Variable
In Exercises 1-6, (a) express (dw)/(dt) as a function of t, both by using
the Chain Rule and by expressing w in terms of t and differentiating
directly with respect to t. Then (b) evaluate (dw)/(dt) at the given value
of t.
1. w = x^2 + y^2, x = cos t, y = sin t; t = π
2. w = x^2 + y^2, x = cos t + sin t, y = cos t - sin t; t = 0
3. w = (x)/(z) + (y)/(z), x = cos^2 t, y = sin^2 t, z = 1/t; t = 3
4. w = ln (x^2 + y^2 + z^2), x = cos t, y = sin t, z = 4√(t);
t = 3

Added by -Ngeles S.

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