Find the Derivative - d/dx sin(8x)

Problem

d(sin(8*x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sin(u) and the inner function is u=8*x

2. Differentiate the outer function with respect to the inner function. The derivative of sin(u) is cos(u)

3. Differentiate the inner function with respect to x The derivative of 8*x is 8

4. Multiply the derivative of the outer function by the derivative of the inner function according to the Chain Rule formula d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

d(sin(8*x))/d(x)=cos(8*x)⋅8

5. Simplify the expression by moving the constant to the front.

d(sin(8*x))/d(x)=8*cos(8*x)

Final Answer

d(sin(8*x))/d(x)=8*cos(8*x)

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