To find : The line of tangent for the function having equation

Answer to Problem 5QR
Explanation of Solution
Given information : The given equation is
Where the value of
Formula used :
Chain Rule:
Product rule:
Power Rule:
Constant Multiply rule:
The given function is
Where
The slope of the tangent line at
So,
First find the first derivative of
The derivative obtained for a sum or difference is the sum or difference of derivatives.
So,
It is noted that the derivative of a constant is always zero.
So,
On using the product rule with
The function
On applying chain rule
The exponential
So.
Returning to the old variable,
Now apply power rule with
Now apply constant multiple rule to the above equation with
On simplification
Therefore gives,
Hence,
Now, to find the slope of the given point
The equation for the tangent line is denoted as
Putting the values, the obtained result is
Or more simply
The equation of the tangent line is
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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