# Trying to find dy/dx of a trig function # 2

• jtt
In summary, the conversation discusses finding the derivative, dy/dx, of the function x + tan(xy) = 0 and the attempt at solving it. The conversation also notes the importance of using parentheses to clarify the placement of variables and making sure to differentiate with respect to the correct variable. It ultimately concludes

find dy/dx

x+tanxy=0

## The Attempt at a Solution

d/dy(x+tanxy)

x+sec^2(xy)((1)(dy/dx))+(1)(tanxy)=0
dy/dx(sec^2(xy)+x+tanxy=0
-x-tanxy -x-tanxy
dy/dx(sec^2(xy)/(sec^2(xy)=(-x-tanxy)/(sec^2(xy))

dy/dx=(-x-tanxy)/(sec^2xy)

jtt said:

find dy/dx

## Homework Equations

x+tanxy=0

You can begin by stating the problem unambiguously. Are you trying to differentiate

x + tan(xy) = 0 or x + ytan(x)=0. The point is that as it is written we can't tell whether the y is inside or outside that tangent function. Parentheses are necessary!

## The Attempt at a Solution

d/dy(x+tanxy)

Why are you writing d/dy when you are differentiating with respect to x?

trying to differentiate x+tan(xy)

i got dy/dx when i took the derivative of y in tan(xy)

jtt said:

find dy/dx

x+tanxy=0

## The Attempt at a Solution

d/dy(x+tanxy)

You mean d/dx(x + tan(xy))

x+sec^2(xy)((1)(dy/dx))+(1)(tanxy)=0
Is the derivative of x equal to x??

And what I highlighted in red should be the derivative of the (xy) which is the argument of the tangent function, or the "inside". There should be no tan(xy) in that.

## 1. What is the process for finding the derivative of a trigonometric function?

The process for finding the derivative of a trigonometric function involves using the rules of differentiation, such as the chain rule and product rule, along with the specific rules for different trigonometric functions. This may also involve simplifying the trigonometric function using identities.

## 2. Can I use the quotient rule to find the derivative of a trigonometric function?

Yes, the quotient rule can be used to find the derivative of a trigonometric function, as long as the function is written in the form of a fraction.

## 3. Are there any special cases or exceptions when finding the derivative of a trigonometric function?

Yes, there are special cases and exceptions when finding the derivative of a trigonometric function. For example, the derivative of the inverse trigonometric functions may require a different set of rules compared to the regular trigonometric functions.

## 4. Is it possible to find the derivative of a trigonometric function without using the rules of differentiation?

No, the rules of differentiation are necessary for finding the derivative of a trigonometric function. However, some trigonometric functions may have simpler derivatives that can be memorized.

## 5. How can I check if my answer for the derivative of a trigonometric function is correct?

You can check if your answer is correct by using the derivative rules to simplify your answer and compare it to the original function. Additionally, you can use graphing software or a graphing calculator to graph both the original function and its derivative and see if they match up.

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