Simple differentiatian of tan question

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In summary, simple differentiation of tan refers to finding the derivative of a tangent function using mathematical formulas. This can be done by applying the basic derivative formula or the quotient rule. The steps for differentiation depend on the method chosen. It is an important concept in calculus and has various applications in different fields.
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Homework Statement


What is the time rate of change of height after 5.0s?

Homework Equations



theta = 3t/(2t + 10)
adjacent length = 1000

Therefore: opposite length (height) h = 1000 tan (3t/(2t+10))

The Attempt at a Solution



I thought it would be simply finding the derivative of the second equation (dh/dt) and plugging in 5 for t.

dh/dt = 1000 * ( sec(3t/(2t+10)) )^2 * [ (2t+10)*3 - 3t(2)/ (2t + 10)^2 ]
dh/dt |t=5 = 1000/(cos.75)^2 * 3/40
= 75.01...

75 m/s

Is this not correct?
 
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  • #2
Change your calculator from degrees to radians. Otherwise, it looks great.
 
  • #3
Thank you. :smile:
 

FAQ: Simple differentiatian of tan question

What is simple differentiation of tan?

Simple differentiation of tan refers to the process of finding the derivative of a tangent function, which is a type of trigonometric function. It involves using mathematical rules and formulas to calculate the rate of change or slope of the tangent curve at a given point.

How do I differentiate tan?

To differentiate tan, you can use the basic derivative formula for trigonometric functions, which is d/dx tan(x) = sec^2(x). This means that the derivative of tangent is equal to the secant squared of the angle x. Alternatively, you can also use the quotient rule to differentiate tan by rewriting it as sin(x)/cos(x) and then applying the rule.

What are the steps to differentiate tan?

The steps to differentiate tan depend on the method you choose. If you use the basic derivative formula, the steps are to identify the angle x, apply the formula d/dx tan(x) = sec^2(x), and simplify the result. If you use the quotient rule, the steps are to rewrite tan as sin(x)/cos(x), apply the rule d/dx f(x)/g(x) = (g(x)f'(x) - f(x)g'(x))/[g(x)]^2, and simplify the result.

Can you provide an example of simple differentiation of tan?

Yes, for example, if we want to differentiate tan(x), we can use the basic derivative formula d/dx tan(x) = sec^2(x). Applying this formula, we get the derivative of tan(x) to be sec^2(x). Similarly, if we use the quotient rule, we can rewrite tan(x) as sin(x)/cos(x) and then apply the rule d/dx f(x)/g(x) = (g(x)f'(x) - f(x)g'(x))/[g(x)]^2 to get the same result of sec^2(x).

Why is simple differentiation of tan important?

Simple differentiation of tan is important because it is a fundamental concept in calculus and is used to solve a variety of mathematical problems in fields such as physics, engineering, and economics. It also helps us understand the behavior of tangent functions and how they change at different points.

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