/ 2 \ sin\x + x + 1/
sin(x^2 + x + 1)
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Differentiate term by term:
Apply the power rule: goes to
Apply the power rule: goes to
The result is:
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
/ 2 \ (1 + 2*x)*cos\x + x + 1/
/ 2\ 2 / 2\ 2*cos\1 + x + x / - (1 + 2*x) *sin\1 + x + x /
/ / 2\ 2 / 2\\ -(1 + 2*x)*\6*sin\1 + x + x / + (1 + 2*x) *cos\1 + x + x //