Given x equals sin 7t and y equals cos 7t, find the following derivatives as functions of t. ...

Question:

Given {eq}x = \sin 7t {/eq} and {eq}y = \cos 7t {/eq} , find the following derivatives as functions of t.

{eq}\frac{dy}{dx} {/eq} AND {eq}\frac{d^2y}{dx^2} {/eq}

Implicit Differentiation:

Whenever the function is in two variables together, we use implicit differentiation. It is a special case of the well-known chain rule for derivatives. If we have to differentiate F(g(x)) w.r.t. the given variable, then we will write its derivative as {eq}F'(g(x))\times g'(x) {/eq}.

Answer and Explanation:


{eq}x = \sin 7t, y=\cos 7t {/eq}

Differentiating we get

{eq}\frac{dx}{dt}= 7\cos 7t, \frac{dy}{dt}= -7\sin 7t {/eq}

The derivative

{eq}\frac{d...

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Learn more about this topic:

Using the Chain Rule to Differentiate Complex Functions

from Math 104: Calculus

Chapter 9 / Lesson 6
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