tan(5*x) + sin(2*x) + sec(x)
tan(5*x) + sin(2*x) + sec(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:
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:
The result is:
Rewrite the function to be differentiated:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
2 5 + 2*cos(2*x) + 5*tan (5*x) + sec(x)*tan(x)
2 / 2 \ / 2 \ -4*sin(2*x) + tan (x)*sec(x) + \1 + tan (x)/*sec(x) + 50*\1 + tan (5*x)/*tan(5*x)
2 / 2 \ 3 2 / 2 \ / 2 \ -8*cos(2*x) + 250*\1 + tan (5*x)/ + tan (x)*sec(x) + 500*tan (5*x)*\1 + tan (5*x)/ + 5*\1 + tan (x)/*sec(x)*tan(x)