Question
derive f(x) = e^2x^2-2x+1
Answers
GPT 3.5
To derive the given function \(f(x) = e^{2x^2} - 2x + 1\), we need to find its derivative with respect to x.
First, differentiate each term separately:
1. The derivative of \(e^{2x^2}\) is \(e^{2x^2} \cdot \frac{d}{dx}(2x^2)\).
Applying the chain rule, we get:
\(\frac{d}{dx}(e^{2x^2}) = e^{2x^2} \cdot 4x = 4xe^{2x^2}\).
2. The derivative of \(-2x\) is \(-2\).
3. The derivative of \(1\) with respect to x is \(0\).
Putting it all together, the derivative of \(f(x)\) is:
\(f'(x) = 4xe^{2x^2} - 2\).
First, differentiate each term separately:
1. The derivative of \(e^{2x^2}\) is \(e^{2x^2} \cdot \frac{d}{dx}(2x^2)\).
Applying the chain rule, we get:
\(\frac{d}{dx}(e^{2x^2}) = e^{2x^2} \cdot 4x = 4xe^{2x^2}\).
2. The derivative of \(-2x\) is \(-2\).
3. The derivative of \(1\) with respect to x is \(0\).
Putting it all together, the derivative of \(f(x)\) is:
\(f'(x) = 4xe^{2x^2} - 2\).