sin(2*y) cos(2*y) e - 3*e
exp(sin(2*y)) - 3*exp(cos(2*y))
Differentiate term by term:
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
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 result of the chain rule is:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
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 of the chain rule is:
So, the result is:
The result is:
The answer is:
sin(2*y) cos(2*y) 2*cos(2*y)*e + 6*e *sin(2*y)
/ 2 sin(2*y) sin(2*y) 2 cos(2*y) cos(2*y)\ 4*\cos (2*y)*e - e *sin(2*y) - 3*sin (2*y)*e + 3*cos(2*y)*e /
/ 3 sin(2*y) sin(2*y) cos(2*y) 3 cos(2*y) cos(2*y) sin(2*y) \ 8*\cos (2*y)*e - cos(2*y)*e - 3*e *sin(2*y) + 3*sin (2*y)*e - 9*cos(2*y)*e *sin(2*y) - 3*cos(2*y)*e *sin(2*y)/