differentiate. f(x)=e^24x f(x)=
differentiate. f(x)=e^24x f(x)=
Answer
Explanation:
Step1: Recall chain - rule
The chain - rule states that if (y = f(g(x))), then (y^\prime=f^\prime(g(x))\cdot g^\prime(x)). Let (u = 24x), so (y = e^{u}).
Step2: Differentiate outer function
The derivative of (y = e^{u}) with respect to (u) is (\frac{dy}{du}=e^{u}).
Step3: Differentiate inner function
The derivative of (u = 24x) with respect to (x) is (\frac{du}{dx}=24).
Step4: Apply chain - rule
By the chain - rule (\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}). Substituting (\frac{dy}{du}=e^{u}) and (\frac{du}{dx}=24) and (u = 24x) back in, we get (\frac{dy}{dx}=e^{24x}\cdot24).
Answer:
(24e^{24x})