Chapter 9: Q. 1 (page 774)

The calculus of parametric equations: Let x = f(t) and y = g(t), where f and g are differentiable functions.
$\frac{d y}{d x} = . . . . . . .$

Short Answer

Expert verified

The value of $\frac{d y}{d x} = \frac{g' (t)}{f' (t)}$

Step by step solution

Step 1. Given information

$x = f (t) y = g (t)$

Step 2. Differentiate functions with respect to t.

$\frac{d x}{d t} = f' (t)$ ........(1)

$\frac{d y}{d t} = g' (t)$ .............(2)

Step 3. Divide equation (2) by (1)

$\frac{d y}{d t} \div \frac{d x}{d t} = \frac{g' (t)}{f' (t)} \frac{d y}{d x} = \frac{g' (t)}{f' (t)}$

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The calculus of parametric equations: Let x = f(t) and y = g(t), where f and g are differentiable functions.
$\frac{d y}{d x} = . . . . . . .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Differentiate functions with respect to t.

Step 3. Divide equation (2) by (1)

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Short Answer

Step by step solution

Step 1. Given information

Step 2. Differentiate functions with respect to t.

Step 3. Divide equation (2) by (1)

One App. One Place for Learning.

Most popular questions from this chapter

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The calculus of parametric equations: Let x = f(t) and y = g(t), where f and g are differentiable functions.
$\frac{d y}{d x} = . . . . . . .$