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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Use implicit differentiation to determine
dy
dx
IL
dy
dx
5
given the equation ³ · y¹ + cos(x) = eª.

Expert Solution

Step 1

The given equation is:

$x^{5} \cdot y^{4} + \cos (x) = e^{y}$

As we know that;

The Sum/Difference rule:

${(f \pm g)}^{'} = f' \pm g'$

The Power law;

$\frac{d}{d x} (x^{n}) = n x^{n - 1}$

The Product rule:

${(f \cdot g)}^{'} = f' \cdot g + f \cdot g'$

And

Use the common derivatives;

$\begin{array}{rcl} \frac{d}{d x} (\cos (x)) & = & - \sin (x) \\ \frac{d}{d x} (e^{x}) & = & e^{x} \end{array}$

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ay Use implicit differentiation to determine given the equation x5y + cos(x) = e". dx dy dx