Mathematics If f(x)=3ex2, then f1(x)−2xf(x)+13f(0)−f1(0) is equal to

$If f (x) = 3 e^{x^{2}}, then f^{1} (x) - 2 x f (x) + \frac{1}{3} f (0) - f^{1} (0) is equal to$

Solution:

$we have f (x) = 3 e^{x^{2}}, differentiating w.r.t.x,we get$

$\begin{array}{l} f^{1} (x) = 6 x e^{x^{2}} \\ f (0) = 3 e^{0} = 3, f^{1} (0) = 6.0 \cdot e^{0} = 0 \\ f^{1} (x) - 2 x f (x) + \frac{1}{3} f (0) - f^{1} (0) \\ = 6 x e^{x^{2}} - 6 x e^{x^{2}} + \frac{1}{3} (3) - 0 = 1 \end{array}$

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