What is the Derivative of (1+tanx)?

In summary, the first derivative of (1+tanx) is equal to (0 + sec^2x * 1) / (sec^2 x). This is derived from the identity 1 = 0, \tan{x}=\sec^2{x}1 = 0, where \frac{\rm d}{{\rm d}x} \tan(x) = \sec^2(x). This identity can be useful for solving problems and making exams easier.
  • #1
fitz_calc
41
0
real quick review needed, I'm working through the quotient rule on a problem and need the first derivative of:

(1+tanx)

is it simply equal to:

(0 + sec^2x * 1)
(sec^2 x)

??
 
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  • #2
yes that's correct

1 = 0, [tex]\tan{x}=\sec^2{x}[/tex]
 
  • #3
rocophysics said:
1 = 0
Geez, that's a nice identity.
I wish I could use that on my exam, it would make life a lot easier :biggrin:
 
  • #4
CompuChip said:
Geez, that's a nice identity.
I wish I could use that on my exam, it would make life a lot easier :biggrin:
lol, you know what i meant ;)
 
  • #5
Yeah, I know you meant

1' = 0, [tex]\tan(x)' = \sec^2(x)[/tex]
where [tex]' = \frac{\rm d}{{\rm d}x}[/tex].
 

What is the derivative of a trigonometric function?

The derivative of a trigonometric function is the rate of change at any given point on the graph of the function. It represents the slope of the tangent line to the function at that point.

What is the general formula for finding the derivative of a trigonometric function?

The general formula for finding the derivative of a trigonometric function is: d/dx(sin(x)) = cos(x) for sine function, d/dx(cos(x)) = -sin(x) for cosine function, and d/dx(tan(x)) = sec^2(x) for tangent function.

How do you find the derivative of a composite trigonometric function?

To find the derivative of a composite trigonometric function, you can use the chain rule. First, find the derivative of the outer function, then multiply it by the derivative of the inner function.

What is the relationship between the derivative of a trigonometric function and its graph?

The derivative of a trigonometric function represents the slope of the tangent line to the function at any given point on its graph. This means that the derivative can help determine the rate of change of the function at that point.

How is the derivative of a trigonometric function used in real life?

The derivative of a trigonometric function is used in various fields such as physics, engineering, and economics. It can help determine the velocity, acceleration, and other important rates of change in real-life scenarios.

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