Finding partial derivative of a trig function

In summary, the conversation discusses finding the partial derivative with respect to x of sin(xyz - 1). The given solution is yz*cos(xyz - 1), but Wolfram Alpha is giving yz*cos(1 - xyz). It is clarified that cos(x) is equivalent to cos(-x) and pressing the "Show steps" button on Wolfram Alpha can help understand the solution.
  • #1
lagwagon555
60
1

Homework Statement



Find the partial derivative with respect to x of sin(xyz - 1)


Homework Equations



None needed.

The Attempt at a Solution



I took the answer to be yz*cos(xyz - 1), but wolfram alpha is giving me yz*cos(1 - xyz). Anyone know what's going on here? Thanks!
 
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  • #2
cos(x) is equal to cos(-x)

Those answers are equivalent.

Btw, if you're confused as to what Wolfram Alpha is doing, press the "Show steps" button. Helps out sometimes.
 
  • #3
Ah right I see, thanks a lot for clarifying that. I'm taking a senior level maths paper after 2 years of not doing maths, so I keep slipping up on things like that. Thanks again :)
 

What is a partial derivative?

A partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables while holding all other variables constant. It is denoted by ∂ (pronounced "partial") and is commonly used in multivariable calculus and physics.

What is a trigonometric function?

Trigonometric functions are mathematical functions that relate an angle of a right triangle to the ratios of the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent. They are widely used in geometry, physics, and engineering.

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

To find the partial derivative of a trigonometric function, you need to use the chain rule of differentiation. First, you take the derivative of the outer function (trigonometric function) and then multiply it by the derivative of the inner function (variable inside the trigonometric function). You also need to use the rules of differentiation for specific trigonometric functions, such as sin, cos, and tan.

Why is finding partial derivatives of trig functions important?

Finding partial derivatives of trig functions is important because it allows us to analyze the rate of change of a function in a specific direction. This is useful in many fields, such as physics, engineering, and economics, where functions often depend on multiple variables.

What are some common mistakes when finding partial derivatives of trig functions?

Some common mistakes when finding partial derivatives of trig functions include forgetting to use the chain rule, making errors in applying the rules of differentiation for specific trigonometric functions, and not simplifying the final result. It is also important to remember to treat all other variables as constants when taking partial derivatives.

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