35 sin (x) sin(5*x) - -------- 3
/ 35 \ d | sin (x)| --|sin(5*x) - --------| dx\ 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:
The derivative of a constant times a function is the constant times the derivative of the function.
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of sine is cosine:
The result of the chain rule is:
So, the result is:
So, the result is:
The result is:
The answer is:
34 35*sin (x)*cos(x) 5*cos(5*x) - ------------------ 3
/ 35 2 33 \ | 7*sin (x) 238*cos (x)*sin (x)| 5*|-5*sin(5*x) + ---------- - --------------------| \ 3 3 /
/ 34 \ | 3 32 721*sin (x)*cos(x)| 5*|-25*cos(5*x) - 2618*cos (x)*sin (x) + -------------------| \ 3 /