differentiate the following function.\n\n$f(x)=e^{4x^{2}-4x}$\n\n$\frac{d}{dx}(e^{4x^{2}-4x})=square$
differentiate the following function.\n\n$f(x)=e^{4x^{2}-4x}$\n\n$\frac{d}{dx}(e^{4x^{2}-4x})=square$
Answer
Explanation:
Step1: Apply the chain rule
The chain rule states that if (y = e^{u}), then (\frac{dy}{dx}=e^{u}\cdot\frac{du}{dx}). Let (u = 4x^{2}-4x).
Step2: Differentiate (u)
Differentiate (u = 4x^{2}-4x) with respect to (x). Using the power rule (\frac{d}{dx}(ax^{n})=nax^{n - 1}), we get (\frac{du}{dx}=\frac{d}{dx}(4x^{2}-4x)=8x - 4).
Step3: Combine results
Since (y = e^{u}) and (u = 4x^{2}-4x), (\frac{dy}{dx}=e^{4x^{2}-4x}\cdot(8x - 4)).
Answer:
((8x - 4)e^{4x^{2}-4x})