What is the derivative of f(x)=2xe^x+(x^2-14)*e^x ?

The derivative of f(x)=2xe^x+(x^2-14)*e^x is e^xx^2+4e^xx-12e^x

What is the first derivative of f(x)=2xe^x+(x^2-14)*e^x ?

The first derivative of f(x)=2xe^x+(x^2-14)*e^x is e^xx^2+4e^xx-12e^x

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derivative of

f (x) = 2 x e^{x} + (x^{2} - 14) \cdot e^{x}

e^{x} x^{2} + 4 e^{x} x - 12 e^{x}

Solution steps

\frac{d}{d x} (2 x e^{x} + (x^{2} - 14) e^{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x e^{x}) + \frac{d}{d x} ((x^{2} - 14) e^{x})

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

\frac{d}{d x} ((x^{2} - 14) e^{x}) = 2 x e^{x} + e^{x} (x^{2} - 14)

= 2 (e^{x} + e^{x} x) + 2 x e^{x} + e^{x} (x^{2} - 14)

Simplify

2 (e^{x} + e^{x} x) + 2 x e^{x} + e^{x} (x^{2} - 14) : e^{x} x^{2} + 4 e^{x} x - 12 e^{x}

= e^{x} x^{2} + 4 e^{x} x - 12 e^{x}

x \to - 2 lim (\frac{1}{x ^{2} - 4})

\int (\frac{1}{x ^{2}} - \frac{1}{x ^{3}}) d x

\frac{d}{d x} (\frac{x ^{5}}{5 - x ^{4}})

- 2

\frac{d}{d x} (ln (x^{2} - 8 x))

What is the derivative of f(x)=2xe^x+(x^2-14)*e^x ?
The derivative of f(x)=2xe^x+(x^2-14)*e^x is e^xx^2+4e^xx-12e^x
What is the first derivative of f(x)=2xe^x+(x^2-14)*e^x ?
The first derivative of f(x)=2xe^x+(x^2-14)*e^x is e^xx^2+4e^xx-12e^x