3 tan (x) - 3*tan(x) + 3*x
tan(x)^3 - 3*tan(x) + 3*x
Differentiate term by term:
Differentiate term by term:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of cosine is negative sine:
Now plug in to the quotient rule:
The result of the chain rule is:
The derivative of a constant times a function is the constant times the derivative of the function.
So, the result is:
The result is:
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 is:
Now simplify:
The answer is:
2 2 / 2 \ - 3*tan (x) + tan (x)*\3 + 3*tan (x)/
3 / 2 \ 12*tan (x)*\1 + tan (x)/
/ 2 \ / 2 \ | / 2 \ 2 4 2 / 2 \| 6*\1 + tan (x)/*\-1 + \1 + tan (x)/ - 3*tan (x) + 2*tan (x) + 7*tan (x)*\1 + tan (x)//