Find the equation of the tangent line to the graph of y(x)=4cot^(6)(x) at x=(pi)/(4). Equation of the tangent line is y=

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Find the equation of the tangent line to the graph of  y(x)=4cot^(6)(x) at  x=(pi)/(4). Equation of the tangent line is  y=

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Find Derivative:  First, we need to find the derivative of y(x) = 4cot^(6)(x) to determine the slope of the tangent line at x = (pi)/(4). Using the chain rule, the derivative y'(x) is given by y'(x) = 4 * 6 * cot^(5)(x) * (-csc^(2)(x)). This simplifies to y'(x) = -24cot^(5)(x)csc^(2)(x) Calculate Slope:  Next, we substitute x = (pi)/(4) into the derivative to find the slope at that point. Since cot((pi)/(4)) = 1 and csc((pi)/(4)) = sqrt(2), we have y'((pi)/(4)) = -24 * 1^(5) * (sqrt(2))^(2) = -24 * 2 = -48 Find y-coordinate:  Now, we find the y-coordinate of the point on the graph at x = (pi)/(4). Substituting x = (pi)/(4) into y(x), we get y((pi)/(4)) = 4 * cot^(6)((pi)/(4)) = 4 * 1^(6) = 4 Use Point-Slope Form:  With the slope of the tangent line and the point (pi/4, 4), we can use the point-slope form of the equation of a line, y - y1 = m(x - x1). Plugging in m = -48, x1 = pi/4, and y1 = 4, the equation becomes y - 4 = -48(x - pi/4) Simplify Equation:  Simplifying the equation, we distribute -48 and rearrange terms to get y = -48x + 12pi + 4

Find the equation of the tangent line to the graph of $y(x)=4 \cot ^{6}(x)$ at $x=\frac{\pi}{4}$ . $\newline$ Equation of the tangent line is $y=$

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Find the equation of the tangent line to the graph of y(x)=4cot⁡6(x) y(x)=4 \cot ^{6}(x) y(x)=4cot6(x) at x=π4 x=\frac{\pi}{4} x=4π​.\newlineEquation of the tangent line is y= y= y=

Find the equation of the tangent line to the graph of $y(x)=4 \cot ^{6}(x)$ at $x=\frac{\pi}{4}$ . $\newline$ Equation of the tangent line is $y=$