sin(4*x) + cos(5*x)
sin(4*x) + cos(5*x)
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 :
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 is:
The answer is:
-5*sin(5*x) + 4*cos(4*x)
-(16*sin(4*x) + 25*cos(5*x))