# Find the Tangent Line at (0,4) y=4e^xcos(x) , (0,4)

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Find and evaluate at and to find the slope of the tangent line at and .
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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.
Reform the equation by setting the left side equal to the right side.
Replace with .
Evaluate at and .
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 (0,4) y=4e^xcos(x) , (0,4)