Video: Differentiating Exponential Functions Using the Chain Rule

If 𝑓(π‘₯) = βˆ’5𝑒^(βˆ’9π‘₯), find 𝑓′(π‘₯).

01:05

Video Transcript

If 𝑓 of π‘₯ is equal to negative five 𝑒 to the negative nine π‘₯, find 𝑓 dash of π‘₯. Find the derivative of the function.

Remember, the derivative of 𝑒 to the power of π‘₯ is 𝑒 to the power of π‘₯. And the derivative of 𝑒 to the power of π‘˜π‘₯ is π‘˜π‘’ to the π‘˜π‘₯. Now, our function is some multiple of 𝑒 to the π‘˜π‘₯. It’s negative five times 𝑒 to the π‘˜π‘₯, where π‘˜ is equal to negative nine. Now, we know that the constant factor rule allows us to take constants outside a derivative and concentrate on differentiating the function of π‘₯ itself. So this means we can say that the derivative of the function of π‘₯ is equal to negative five times the derivative of 𝑒 to the negative nine π‘₯. And we know that the derivative of 𝑒 to the negative nine π‘₯ is negative nine times 𝑒 to the negative nine π‘₯. And since negative five multiplied by negative nine is 45, we can say that the derivative of our function is 45𝑒 to the negative nine π‘₯.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.