What is the derivative of 2xe^{x-1}+e^{x-1}(x^2+1) ?

The derivative of 2xe^{x-1}+e^{x-1}(x^2+1) is e^{x-1}x^2+4e^{x-1}x+3e^{x-1}

What is the first derivative of 2xe^{x-1}+e^{x-1}(x^2+1) ?

The first derivative of 2xe^{x-1}+e^{x-1}(x^2+1) is e^{x-1}x^2+4e^{x-1}x+3e^{x-1}

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derivative of

2 x e^{x - 1} + e^{x - 1} (x^{2} + 1)

e^{x - 1} x^{2} + 4 e^{x - 1} x + 3 e^{x - 1}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 2 (e^{x - 1} + e^{x - 1} x) + e^{x - 1} (x^{2} + 1) + 2 x e^{x - 1}

Simplify

2 (e^{x - 1} + e^{x - 1} x) + e^{x - 1} (x^{2} + 1) + 2 x e^{x - 1} : e^{x - 1} x^{2} + 4 e^{x - 1} x + 3 e^{x - 1}

= e^{x - 1} x^{2} + 4 e^{x - 1} x + 3 e^{x - 1}

\int (e^{3 x} - 4)^{5} \cdot 3 e^{3 x} d x

\int arccot (9 y) d y

\frac{d ^{2}}{d x ^{2}} ((x^{3} + 8) e^{x})

\frac{d}{d x} (r (x) x)

x \cdot e^{x}

What is the derivative of 2xe^{x-1}+e^{x-1}(x^2+1) ?
The derivative of 2xe^{x-1}+e^{x-1}(x^2+1) is e^{x-1}x^2+4e^{x-1}x+3e^{x-1}
What is the first derivative of 2xe^{x-1}+e^{x-1}(x^2+1) ?
The first derivative of 2xe^{x-1}+e^{x-1}(x^2+1) is e^{x-1}x^2+4e^{x-1}x+3e^{x-1}