Find the derivative of the function. f(t)=cosh(e^t^2) |...

Name: Problem 8, Chapter 3: Calculus Single Variable
Uploaded: 2021-04-27T07:32:30-08:00
Duration: 1 min 11 s
Channel: Tyler Moulton
Description: Find the derivative of the function. f(t)=cosh(e^t^2)

Key Concepts

Chain Rule

The chain rule is a fundamental principle in calculus used for differentiating composite functions. It states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function. This concept is crucial when dealing with functions where one function is nested within another, as is the case with the cosine hyperbolic of an exponential function.

Derivatives of Hyperbolic Functions

Hyperbolic functions, such as cosh and sinh, have derivatives that are analogous to their trigonometric counterparts. Knowing that the derivative of cosh(x) is sinh(x) is essential when differentiating functions involving hyperbolic expressions, especially when they are composed with other functions.

Derivatives of Exponential Functions

Exponential functions are ubiquitous in calculus, and their differentiation follows a specific rule: the derivative of e^u, where u is a function of t, is e^u multiplied by the derivative of u. This rule is important when the argument of the exponential function is not simply t but a more complex function like t^2.

Power Rule

The power rule is a basic differentiation technique used when dealing with functions that involve exponents. It states that the derivative of t raised to a constant exponent is the exponent multiplied by t raised to one less than that exponent. This rule is especially useful when differentiating terms like t^2, which often appear within more complex functions.

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