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Find an equation of the tangent line to the curve y=sin(5x) cos(6x)

User Khaaliq
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Final answer:

To find the equation of the tangent line to the curve y = sin(5x)cos(6x) at a specific point, we need to find the derivative of the curve and evaluate it at the given point. Once we have the slope, we can use the point-slope form of a line to find the equation of the tangent line.

Step-by-step explanation:

To find the equation of the tangent line to the curve y = sin(5x)cos(6x) at a specific point, we need to find the derivative of the curve. Let's start by finding the derivative of y with respect to x:

y' = (d/dx)[sin(5x)cos(6x)]

Using the product rule and the chain rule, we can simplify the derivative to:

y' = 5cos(5x)cos(6x) - 6sin(5x)sin(6x)

Now, evaluate y' at the given point to find the slope of the tangent line. Substitute x = 25 into the equation for y' to get the slope:

y'(25) = 5cos(125)cos(150) - 6sin(125)sin(150)

Simplify the expression to find the slope of the tangent line at x = 25. Once you have the slope, you can use the point-slope form of a line, y - y₁ = m(x - x₁), to find the equation of the tangent line.

User SilithCrowe
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