use implicit differentiation to find an equation of the tangent line to the graph at the given p

step 1 Question is find the equation of the tangent if the given equation is x plus y minus 1 equals to

Use implicit differentiation to find an equation of the...

Key Concepts

Differentiation of Logarithmic Functions

Differentiating functions involving logarithms, such as the natural logarithm, requires applying the rule that the derivative of ln(u) is u'/u. This is essential when handling equations in which logarithms are present and the argument of the logarithm is a function of x and y.

Evaluation at a Point

After obtaining a general expression for the derivative through implicit differentiation, the next step involves substituting the specific coordinates of the point of interest. This evaluation yields the slope of the tangent line at that point, which is then used to construct the tangent line equation using the point-slope form.

Chain Rule

The chain rule is used when differentiating composite functions. When y is considered a function of x, any term involving y inside another function must be differentiated using the chain rule, which accounts for the derivative of y with respect to x.

Implicit Differentiation

Implicit differentiation is a method used to differentiate equations where y is defined implicitly in terms of x. Instead of solving for y explicitly, both sides of the equation are differentiated with respect to x, treating y as a function of x and applying the chain rule when necessary.

Tangent Line

A tangent line is a straight line that touches a curve at a single point and shares the same slope as the curve at that point. Finding the tangent line typically requires computing the derivative of the function at the given point and using the point-slope form to express the line.

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