4 tan(4*x) - 2*x - 10*x
tan(4*x) - 2*x^4 - 10*x
Differentiate term by term:
Differentiate term by term:
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:
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:
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:
3 2 -6 - 8*x + 4*tan (4*x)
/ 2 / 2 \ \ 8*\- 3*x + 4*\1 + tan (4*x)/*tan(4*x)/
/ 2 \ | / 2 \ 2 / 2 \| 16*\-3*x + 8*\1 + tan (4*x)/ + 16*tan (4*x)*\1 + tan (4*x)//
/ 2 \ | / 2 \ 2 / 2 \| 16*\-3*x + 8*\1 + tan (4*x)/ + 16*tan (4*x)*\1 + tan (4*x)//