3 sin (2*x) + 4*sin(2*x) 3
/ 3 \ d | sin (2*x) + 4*sin(2*x)| --\3 / dx
Let .
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
The result of the chain rule is:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
So, the result is:
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
3 sin (2*x) + 4*sin(2*x) / 2 \ 3 *\8*cos(2*x) + 6*sin (2*x)*cos(2*x)/*log(3)
/ 2 \ / 2 \ \4 + sin (2*x)/*sin(2*x) | / 2 2 \ / 2 \ 2 | 4*3 *\- \4 - 6*cos (2*x) + 3*sin (2*x)/*sin(2*x) + \4 + 3*sin (2*x)/ *cos (2*x)*log(3)/*log(3)
/ 2 \ / 3 \ \4 + sin (2*x)/*sin(2*x) | 2 2 / 2 \ 2 2 / 2 \ / 2 2 \ | 8*3 *\-4 - 21*sin (2*x) + 6*cos (2*x) + \4 + 3*sin (2*x)/ *cos (2*x)*log (3) - 3*\4 + 3*sin (2*x)/*\4 - 6*cos (2*x) + 3*sin (2*x)/*log(3)*sin(2*x)/*cos(2*x)*log(3)