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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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In Exercises 7 and 8, find d y / d x

implicitly.

y 2 + x y = 7

To determine

To calculate: The value of dydx for the equation y2+xy=10 using the implicit differentiation.

Explanation

Given information:

The provided equation is y2+xy=10.

Formula used:

Product rule of derivative of differentiable functions, f(x) and g(x) is:

ddx[f(x)g(x)]=f(x)g(x)+f(x)g(x).

The derivative of function f(x)=un using the chain rule is:

f(x)=ddx(un)=nun1dudx

Where, u is the function of x.

Calculation:

Consider the equation,

y2+xy=10

Take ddx of both sides of the above equation,

ddx(y2+xy)=ddx(7)

Apply product rule of derivative to function xy,

ddx(y2)+ddx</

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