sin(5*x) + cos(2*x - 3)
sin(5*x) + cos(2*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:
-2*sin(2*x - 3) + 5*cos(5*x)
-(4*cos(-3 + 2*x) + 25*sin(5*x))
-125*cos(5*x) + 8*sin(-3 + 2*x)