What is the derivative of f(x)e^{-(x-2)^2}+3 ?

The derivative of f(x)e^{-(x-2)^2}+3 is e^{-x^2+4x-4}x

What is the first derivative of f(x)e^{-(x-2)^2}+3 ?

The first derivative of f(x)e^{-(x-2)^2}+3 is e^{-x^2+4x-4}x

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derivative of

f (x) e^{- (x - 2)^{2}} + 3

e^{- x^{2} + 4 x - 4} x

Solution steps

\frac{d}{df} (f x e^{- (x - 2)^{2}} + 3)

Simplify

f x e^{- (x - 2)^{2}} + 3 : e^{- x^{2} + 4 x - 4} f x + 3

= \frac{d}{df} (e^{- x^{2} + 4 x - 4} f x + 3)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{df} (e^{- x^{2} + 4 x - 4} f x) + \frac{d}{df} (3)

\frac{d}{df} (e^{- x^{2} + 4 x - 4} f x) = x e^{- x^{2} + 4 x - 4}

\frac{d}{df} (3) = 0

= x e^{- x^{2} + 4 x - 4} + 0

Simplify

= e^{- x^{2} + 4 x - 4} x

\int sin^{3} (φ) d φ

\int_{- e}^{e} \frac{1}{∣ x ∣} d x

1 + 2 x

\int \frac{x ^{2} + 1}{x ( x ^{2} - 1 )} d x

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What is the derivative of f(x)e^{-(x-2)^2}+3 ?
The derivative of f(x)e^{-(x-2)^2}+3 is e^{-x^2+4x-4}x
What is the first derivative of f(x)e^{-(x-2)^2}+3 ?
The first derivative of f(x)e^{-(x-2)^2}+3 is e^{-x^2+4x-4}x