# Math Sc E Derivative Of Chain Rule (Video), Simple Examples Of Using The Chain Rule

I need help with exponential functions. I know that the derivative of \$e^x\$ is \$e^x\$, but wolfram alpha shows a different answer to my function below. If you, for example, take the derivative of \$e^{-2x}\$ do you get \$-2e^{-2x}\$ or \$e^{-2x}\$?

You have to apply the chain rule: if \$f(x)\$ is a differentiable function then the derivative of \$e^{f(x)}\$ is \$f”(x)e^{f(x)}\$.

Đang xem: E derivative of chain rule

You have to use the chain rule here. Writing \$f(x) = e^x\$ and \$g(x) = -2x\$ we have \$h(x) := f(g(x)) = e^{-2x}\$, hence by the chain rule\$\$ h”(x) = f”(g(x))g”(x) \$\$Now \$f”(x) = e^x\$, hence \$f”(g(x)) = e^{-2x}\$, and \$g”(x) = -2\$, this gives\$\$ h”(x) = f”(g(x))g”(x) = e^{-2x} cdot (-2) = -2e^{-2x} \$\$

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