tan(x) - 4*x
d --(tan(x) - 4*x) dx
Differentiate term by term:
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 derivative of a constant times a function is the constant times the derivative of the function.
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:
So, the result is:
The result is:
Now simplify:
The answer is:
/ 2 \ 2*\1 + tan (x)/*tan(x)
/ 2 \ / 2 \ 2*\1 + tan (x)/*\1 + 3*tan (x)/