How to Differentiate z with Respect to ∅?

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SUMMARY

The discussion focuses on differentiating the function z = ((A+B)/2) + ((A-B)/2)Cos(2∅) + C Sin(2∅) with respect to ∅. The correct result is established as Tan(2∅) = (2C)/(A-B) when dz/d∅ equals zero. The differentiation process involves calculating dz/d∅ and setting it to zero, leading to the equation 0 = -(A-B)tan(2∅) + 2C. The user seeks clarification on the differentiation steps to achieve this result.

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  • Understanding of basic calculus concepts, specifically differentiation.
  • Familiarity with trigonometric identities, particularly tangent and cosine functions.
  • Knowledge of algebraic manipulation to solve equations.
  • Experience with functions involving multiple variables.
NEXT STEPS
  • Study the process of differentiation in calculus, focusing on trigonometric functions.
  • Learn about solving trigonometric equations, particularly those involving tangent and sine.
  • Explore the application of the chain rule in differentiation.
  • Review examples of differentiating composite functions to strengthen understanding.
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Students studying calculus, mathematics educators, and anyone looking to improve their skills in differentiating trigonometric functions.

hatchelhoff
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I am having trouble Differentiating the following with respect to ∅. Can you show me the steps I need to take to get the given correct answer please.

z = ((A+B)/2) + ((A-B)/2)Cos2∅ + C Sin2∅


The correct answer is
Tan2∅ = (2C)/(A-B)
 
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for your answer to be true, dz/d(theta) has to equal zero.

differentiating: dz/d(theta)=0-(A-B)sin(2∅)+2Ccos(2∅)
if dz/d∅=0, then divide by cos(2∅) on both sides and you'l get

0=-(A-B)tan(2∅)+2C

solve for tan and you'll get tan(2∅)=(2C)/(A-B)
 
Thanks Physeven
can you explain to me in more detail how you got the line
please. Its the actual process of differentiation I am having trouble with.

dz/d(theta)=0-(A-B)sin(2∅)+2Ccos(2∅)
 

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