Find the derivative of the function. Simplify where...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Chain Rule

The chain rule is a fundamental concept in calculus used to differentiate composite functions. It allows one to differentiate a function that is applied to another function by taking the derivative of the outer function evaluated at the inner function and then multiplying this by the derivative of the inner function.

Derivative of the Exponential Function

The derivative of an exponential function, where the base is Euler's number e, is unique in that it is proportional to the function itself. When the exponent is a function of the variable, the chain rule is applied along with the standard exponential derivative rule.

Derivative of the Inverse Trigonometric Function

Inverse trigonometric functions, such as arcsin, have specific derivative formulas. Their derivatives generally involve expressions that include radicals to account for the implicit trigonometric relationship, and when combined with the chain rule, these derivatives address the rate of change of a composition involving an inverse trigonometric function.

Transcript

Please give Ace some feedback