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Question: What is the derivative of f(t)=t4+92 ?

Use a x n = a x n to rewrite t 4 + 9 as ( t 4 + 9 ) 1 2 .

d d t [ ( t 4 + 9 ) 1 2 ]

Differentiate using the chain rule, which states that d d t [ f ( g ( t ) ) ] is f ′ ( g ( t ) ) g ′ ( t ) where f ( t ) = t 1 2 and g ( t ) = t 4 + 9 .

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Thyroid Test Analyzer: Decode Your Results

This thyroid test analyzer will help you understand your TSH, T3, T4, and other thyroid function test results. Select a test and enter your lab value to learn more. “This tool is aimed to help you interpret your thyroid function test in order to clarify your diagnosis or track the progression of treatment. Please make sure you discuss with your doctor your concerns or questions.” – Ana Maria Kausel, MD .

Helpful Resources

Thyroid disease is common yet often misunderstood or overlooked. If your thyroid test results are outside of the optimal range—or if you’ve been diagnosed with hyperthyroidism , hypothyroidism , Graves’ disease, Hashimoto’s thyroiditis , or another thyroid-related condition—Verywell offers free resources to help you better understand and manage your condition. We want to help ensure you have productive and empowering discussions with your physicians.

Explore the following articles, tools, downloads, and communities to learn more:

• Read more about thyroid disease
• Read more about thyroid function tests and results
• Download the Thyroid Disease Doctor Discussion Guide
• Join the Real Life With Thyroid Disease Facebook Community

Frequently Asked Questions

What information do i need in order to get my thyroid test analysis.

All you need is the name of the test and the test value, as listed on your thyroid test results report that you receive from your doctor. You’ll need to provide both pieces of information to receive an analysis.

All test values should be numerical values—no need to add units, we’ll add those for you!

Which thyroid tests can be analyzed?

Our tool can analyze results from these common thyroid function tests:

• Thyroid stimulating hormone (TSH)
• Free thyroxine (Free T4)
• Free triiodothyronine (Free T3)
• Radioactive iodine uptake (RAIU) at 6 and 24 hours
• TRH stimulation test
• Thyroglobulin antibody
• Thyroid peroxidase antibodies (TPO)
• Thyroid Stimulating Immunoglobulins (TSI)
• Thyrotropin receptor antibodies (TRAb)

It will also analyze results from these thyroid tests that have been largely replaced but are still used in some practices:

• Total thyroxine (T4)
• Total triiodothyronine (T3)
• Free thyroxin index (FTI)
• T3 resin uptake (T3RU)
• Thyroid binding globulin (TBG), measured by electrophoresis and radioimmunoassay

You can analyze one test at a time. Remember, however, that many of these tests are related and the various thyroid hormones interact with each other and are affected by multiple factors . Your doctor is the best person to analyze your results as a whole—this tool is meant for informational purposes only.

Download this guide for a full overview of each thyroid function test, its optimal range, and what the results mean.

Download: Understanding the Various Thyroid Function Tests

Where can I find my thyroid test results or lab report?

In most cases, your test results will be ready a few days after your bloodwork or imaging test. You can obtain a copy from your doctor’s office, either at a visit or by calling in.

Your doctor will have the results even if the tests were performed outside of their office. They will likely call or schedule an appointment to review them with you. You can use this tool before or after your discussion to learn more about the different tests and results.

Some labs and offices also offer online patient portals where you can view your results without having to call in. Select the name of the test, as indicated on your report, and enter it into the analyzer, along with your listed numerical value, to receive an analysis.

Note that different laboratories may have different reference ranges for these tests. The reference ranges used in the analyzer are meant to represent typical ranges. If the ranges differ, you should refer to the specific ones provided by the laboratory in which the test was performed.

What information will I receive from the tool?

Once you enter your information, the thyroid function test analyzer will tell you if your result is low, optimal, or high and what that might mean. You’ll also learn a little bit about the test, why it’s done, and what it measures.

Patients with thyroid cancer, pregnancy or pituitary disorders must seek a specialist's care.

How were the results analyzed?

Your results analysis was completed by a board-certified physician. Optimal range values and interpretations are in line with leading thyroid authorities (although they sometimes slightly vary across laboratories).

Remember, however, that this analysis is for informational purposes only. You should use it as a starting point or to further understand what you have already discussed with your doctor. It is not a replacement for a professional medical visit.

Thyroid conditions and hormones are complicated and test results may be affected by multiple factors . Your doctor is the best person to take a holistic look at you, your medical history, and the relationships between your different thyroid hormones. They can provide you with the most customized, accurate interpretation and next steps to follow.

Who else can see my lab results or personal analysis?

We take online privacy very seriously, especially when it comes to individual and personalized health information. We do not track which lab tests you analyze and we do not store any lab values you enter. You are the only one who can see your analysis. Also, you will not be able to return to your results, so if you would like to save them it is best to print them.

Please see our Privacy Policy for more information.

Can this tool diagnose me with a thyroid condition?

This tool does not provide medical advice or diagnosis. It is intended for informational purposes only and is not a substitute for professional medical consultations, diagnosis, or treatment.

What should I do with the analysis?

You should use the analysis to empower yourself and learn more about your results, but not to diagnose yourself with a thyroid-related condition, such as hyperthyroidism , hypothyroidism , Graves’ disease, or Hashimoto’s thyroiditis . Proper diagnosis and treatment require a holistic look at your previous medical history, symptoms, lifestyle, and more. Your doctor is the best person to do this.

You can use this information to inspire questions or use it as a starting point for a conversation with your doctor at your next appointment. Asking the right questions can help you know what to expect.

Also, consider bringing along a doctor discussion guide for even more guidance—it lists common vocabulary terms your doctor may use and important questions about symptoms, causes, diagnosis, treatment, and living well with thyroid disease.

Download: Thyroid Disease Doctor Discussion Guide