5*sin(10*x) - 3 --------------- 100
(5*sin(10*x) - 3)/100
The derivative of a constant times a function is the constant times the derivative of the function.
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 the constant is zero.
The result is:
So, the result is:
The answer is: