Question

I am wondering how to do the following problem: find an equation of the tangent line to the curve given the point:
y=(sinx)+(sin^2)x point= (0,0)

Answer 1

\(\large ?\)

Answer 2

To get a line, you need a point and a slope. We have the point; what's the slope? Well, we determine that by evaluating the derivative of the function at that point. In this case, dy/dx = cos(x) + 2sin(x)cos(x); evaluated at (0,0) is 1. So plugging into point slope, y-y0 = m(x-x0) gives y = x

Answer 3

thank you! but I don't understand how you found the derivative

Answer 4

Take it term by term. The derivative of sin(x) is cos(x). The derivative of sin^2(x) = [sin(x)]^2 is done by chain rule. We take the derivative of the outside and multiply it by the derivative of the inside - 2*sin(x) * [derivative of sin(x)] = 2sin(x)cos(x)

Answer 5

chain rule right ! thank you !!