Chain Rule for Derivative of sin(2 x)
Description
This illustrates the relations between the derivatives of sin(x) and sin(2x).
Step 1: This shows sin(2x) and the point x which can be moved. A dot on the curve is located at ( x, sin(2x))
Step 2: The definitions of the outside function and the inside function for the chain rule are added. Note that the slopes are not as steep as the function.
Step 3: The outside function is graphed as a function of the inside function. The Point on the curve ( 2x, sin(2x) ) is also indicated with a black dot.
Step 4: The tangent lines at the two black dots are shown. Note that the slope of the green tangent line is less than the slope of the red dashed line.
Step 5: For the full chain rule, the slope of the green dashed line need to be multiplied by the derivative of the inside function of the chain rule. Note that the slope of the purple long dashed line is the same as the slope of the red dashed line, that is the derivatives are the same.