The derivative of tan(x) can be found using the quotient rule:
Let y = tan(x)
Then y’ = (sec^2(x))(1) – (tan(x))(sec^2(x))(1)
Simplifying this expression, we get:
y’ = sec^2(x) – tan^2(x)
Since 1 + tan^2(x) = sec^2(x) (by the Pythagorean identity), we can replace tan^2(x) with sec^2(x) – 1:
y’ = sec^2(x) – (sec^2(x) – 1)
y’ = 1
Therefore, the derivative of tan(x) is simply 1.
[next_post_link]
Share:
How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing
Ramses II (c. 1279–1213 BCE) Ramses II, also known as Ramses the Great, was one of the most prominent and powerful pharaohs of ancient Egypt.
Is the formula of cyclic adenosine monophosphate (cAMP) $ce{C_{10}H_{11}N_{5}O_{6}P}$ or $ce{C_{10}H_{12}N_{5}O_{6}P}$? Does it matter? The correct formula for cyclic adenosine monophosphate (cAMP) is $ce{C_{10}H_{11}N_{5}O_{6}P}$. The
How does a turtle develop inside its egg? The development of a turtle inside its egg is a fascinating process that involves several stages and
Why does photosynthesis specifically produce glucose? Photosynthesis is the biological process by which plants, algae, and some bacteria convert sunlight, carbon dioxide (CO2), and water
