# Find the Tangent Line at the Point 8e^xcos(x) , (0,8)

,
Find the derivative.
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Simplify the expression.
Move to the left of .
Rewrite as .
Differentiate using the Exponential Rule which states that is where =.
Simplify.
Apply the distributive property.
Multiply by .
Reorder terms.
Replace the variable with in the expression.
Simplify each term.
Anything raised to is .
Multiply by .
The exact value of is .
Multiply by .
Anything raised to is .
Multiply by .
The exact value of is .
Multiply by .
Plug in the slope of the tangent line and the and values of the point into the pointslope formula .
Simplify.
The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
Multiply by .
Subtract from .
Add to both sides of the equation.
Find the Tangent Line at the Point 8e^xcos(x) , (0,8)