tan(x) -------- 2 (x - 2)
tan(x)/(x - 2)^2
Apply the quotient rule, which is:
and .
To find :
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:
To find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
The result of the chain rule is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 1 + tan (x) (4 - 2*x)*tan(x) ----------- + ---------------- 2 4 (x - 2) (x - 2)
/ / 2 \ \ |/ 2 \ 2*\1 + tan (x)/ 3*tan(x)| 2*|\1 + tan (x)/*tan(x) - --------------- + ---------| | -2 + x 2| \ (-2 + x) / ------------------------------------------------------ 2 (-2 + x)
/ / 2 \ / 2 \ \ |/ 2 \ / 2 \ 12*tan(x) 9*\1 + tan (x)/ 6*\1 + tan (x)/*tan(x)| 2*|\1 + tan (x)/*\1 + 3*tan (x)/ - --------- + --------------- - ----------------------| | 3 2 -2 + x | \ (-2 + x) (-2 + x) / ---------------------------------------------------------------------------------------- 2 (-2 + x)