3*sin(2*x) - 5*cos(2*x)
3*sin(2*x) - 5*cos(2*x)
Differentiate term by term:
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 derivative of a constant times a function is the constant times the derivative of the function.
Let .
The derivative of cosine is negative sine:
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 answer is:
6*cos(2*x) + 10*sin(2*x)
4*(-3*sin(2*x) + 5*cos(2*x))
-8*(3*cos(2*x) + 5*sin(2*x))