sin(4*x) + cos(3*x - 3)
sin(4*x) + cos(3*x - 3)
Differentiate term by term:
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:
Let .
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by :
Differentiate term by term:
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 derivative of the constant is zero.
The result is:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
-3*sin(3*x - 3) + 4*cos(4*x)
-(9*cos(3*(-1 + x)) + 16*sin(4*x))