How do you find the equation of the tangent line to graph #y=(lnx)^cosx# at the point #(e, 1)#?
The equation is
We can differentiate the entire function using the product rule.
We now determine the equation of the tangent line.
Hopefully this helps!
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To find the equation of the tangent line to the graph of y = (lnx)^cosx at the point (e, 1), we need to find the slope of the tangent line and then use the pointslope form of a linear equation.

Find the derivative of the function y = (lnx)^cosx using the chain rule: dy/dx = (cosx * (lnx)^(cosx1) * (1/x))  ((lnx)^cosx * sinx)

Evaluate the derivative at x = e: dy/dx = (cos(e) * (ln(e))^(cos(e)1) * (1/e))  ((ln(e))^cos(e) * sin(e))

Simplify the expression: dy/dx = (cos(e) * (1/e))  ((ln(e))^cos(e) * sin(e))

Substitute the xcoordinate of the given point (e, 1) into the derivative to find the slope: m = (cos(e) * (1/e))  ((ln(e))^cos(e) * sin(e))

Use the pointslope form of a linear equation, y  y1 = m(x  x1), where (x1, y1) is the given point (e, 1): y  1 = m(x  e)

Simplify the equation: y  1 = [(cos(e) * (1/e))  ((ln(e))^cos(e) * sin(e))](x  e)
This is the equation of the tangent line to the graph of y = (lnx)^cosx at the point (e, 1).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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