Question

Find an equation for the tangent line to the curve y=sin⁡xy=sinx at x=1x=1.

A. y=x+1
B. y=−x−1
C. y=1
D. y=−x+1

Answer 1

To find the equation for the tangent line to the curve y = sin(xy) at x = 1, we need to find the derivative of the function with respect to x and evaluate it at x = 1. The derivative of sin(xy) with respect to x can be found using the chain rule, and the equation for the tangent line is y = cos(y) * (y + y').

Step-by-step explanation:

To find the equation for the tangent line to the curve y = sin(xy) at x = 1, we need to find the derivative of the function with respect to x and evaluate it at x = 1. The derivative of sin(xy) with respect to x can be found using the chain rule: d/dx[sin(xy)] = d/dx[sin(xy)] * dy/dx = cos(xy) * (y + xy').

Now, we substitute x = 1 into the equation: cos(1 * y) * (y + y') = cos(y) * (y + y').

Therefore, the equation for the tangent line to the curve y = sin(xy) at x = 1 is y = cos(y) * (y + y').