What is the derivative of 3x^2e^x+e^x(x^3+8) ?

The derivative of 3x^2e^x+e^x(x^3+8) is e^xx^3+6e^xx^2+6e^xx+8e^x

What is the first derivative of 3x^2e^x+e^x(x^3+8) ?

The first derivative of 3x^2e^x+e^x(x^3+8) is e^xx^3+6e^xx^2+6e^xx+8e^x

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

e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 8 e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 8) + 3 x^{2} e^{x}

Simplify

3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 8) + 3 x^{2} e^{x} : e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 8 e^{x}

= e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 8 e^{x}

\frac{d}{d y} (\frac{y ^{3}}{3})

x \to 1 - lim (∣ x ∣)

y^{^{'}} = 0.0015 y (2700 - y)

\frac{d}{d x} ((\frac{x}{1 + x})^{5})

f (x) = 4 - x, - 2, 6

What is the derivative of 3x^2e^x+e^x(x^3+8) ?
The derivative of 3x^2e^x+e^x(x^3+8) is e^xx^3+6e^xx^2+6e^xx+8e^x
What is the first derivative of 3x^2e^x+e^x(x^3+8) ?
The first derivative of 3x^2e^x+e^x(x^3+8) is e^xx^3+6e^xx^2+6e^xx+8e^x