2*tan(3*x) + 3*tan(2*x)
2*tan(3*x) + 3*tan(2*x)
Differentiate term by term:
The derivative of a constant times a function is the constant times the derivative of the function.
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
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:
To find :
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:
Now plug in to the quotient rule:
So, the result is:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
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 result is:
Now simplify:
The answer is:
2 2 12 + 6*tan (2*x) + 6*tan (3*x)
/ / 2 \ / 2 \ \ 12*\2*\1 + tan (2*x)/*tan(2*x) + 3*\1 + tan (3*x)/*tan(3*x)/
/ 2 2 \ | / 2 \ / 2 \ 2 / 2 \ 2 / 2 \| 12*\4*\1 + tan (2*x)/ + 9*\1 + tan (3*x)/ + 8*tan (2*x)*\1 + tan (2*x)/ + 18*tan (3*x)*\1 + tan (3*x)//
/ 2 2 \ | / 2 \ / 2 \ 2 / 2 \ 2 / 2 \| 12*\4*\1 + tan (2*x)/ + 9*\1 + tan (3*x)/ + 8*tan (2*x)*\1 + tan (2*x)/ + 18*tan (3*x)*\1 + tan (3*x)//