# How do you find the equation of the tangent line to the curve #y = x sin x# at the point where x = π/2?

Differentiate the function with the product rule.

Differentiation will give you the gradient for the tangent at any point, and you use the product rule whenever a function can be thought of as two functions multiplied together.

Therefore, we can say that

Now we substitute this into the equation we already have for the tangent,

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To find the equation of the tangent line to the curve y = x sin x at the point where x = π/2, we need to find the slope of the tangent line and the coordinates of the point of tangency.

First, we find the derivative of the function y = x sin x using the product rule. The derivative is given by dy/dx = sin x + x cos x.

Next, we substitute x = π/2 into the derivative to find the slope of the tangent line at that point. The slope is dy/dx = sin(π/2) + (π/2) cos(π/2) = 1 + (π/2)(0) = 1.

Now, we have the slope of the tangent line. To find the coordinates of the point of tangency, we substitute x = π/2 into the original function y = x sin x. The y-coordinate is y = (π/2) sin(π/2) = (π/2)(1) = π/2.

Therefore, the point of tangency is (π/2, π/2) and the slope of the tangent line is 1. Using the point-slope form of a line, the equation of the tangent line is y - π/2 = 1(x - π/2), which simplifies to y = x - π/2.

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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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