# How do you find the equation of the tangent line to graph #y=x^sinx# at the point #(pi/2, pi/2)#?

The equation of the tangent line is

Now, use the product rule and implicit differentiation to find the derivative.

Now, we use point-slope form to find the equation of the line.

Hopefully this helps!

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To find the equation of the tangent line to the graph of y = x^sinx at the point (pi/2, pi/2), we need to find the slope of the tangent line at that point.

First, we find the derivative of the function y = x^sinx using the product rule and chain rule. The derivative is given by:

dy/dx = sinx * x^(sinx-1) + x^sinx * cosx * ln(x)

Next, we substitute x = pi/2 into the derivative to find the slope at the point (pi/2, pi/2).

dy/dx = sin(pi/2) * (pi/2)^(sin(pi/2)-1) + (pi/2)^sin(pi/2) * cos(pi/2) * ln(pi/2)

Simplifying this expression, we get:

dy/dx = 1 * (pi/2)^(1-1) + (pi/2) * 0 * ln(pi/2)

dy/dx = (pi/2)^0

dy/dx = 1

Therefore, the slope of the tangent line at the point (pi/2, pi/2) is 1.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y1 = m(x - x1)

Substituting the values of (pi/2, pi/2) and the slope m = 1, we have:

y - pi/2 = 1(x - pi/2)

Simplifying this equation, we get:

y = x - pi/2 + pi/2

y = x

Hence, the equation of the tangent line to the graph of y = x^sinx at the point (pi/2, pi/2) is y = x.

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When evaluating a one-sided 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 one-sided 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 one-sided 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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