What is the derivative of 3x^2e^x+e^x(x^3+7) ?

The derivative of 3x^2e^x+e^x(x^3+7) is e^xx^3+6e^xx^2+6e^xx+7e^x

What is the first derivative of 3x^2e^x+e^x(x^3+7) ?

The first derivative of 3x^2e^x+e^x(x^3+7) is e^xx^3+6e^xx^2+6e^xx+7e^x

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derivative of

3 x^{2} e^{x} + e^{x} (x^{3} + 7)

e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 7 e^{x}

Solution steps

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 7))

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} + 7))

\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} + 7)) = e^{x} (x^{3} + 7) + 3 x^{2} e^{x}

= 3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 7) + 3 x^{2} e^{x}

Simplify

3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 7) + 3 x^{2} e^{x} : e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 7 e^{x}

= e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 7 e^{x}

f (x) = x^{2} + x, at x = - 3

y^{^{'}} + y = cos (t)

x \to - \infty lim (3)

\frac{d}{d x} (3^{s i n (3 x)})

\int \frac{x}{4 + x} d x

What is the derivative of 3x^2e^x+e^x(x^3+7) ?
The derivative of 3x^2e^x+e^x(x^3+7) is e^xx^3+6e^xx^2+6e^xx+7e^x
What is the first derivative of 3x^2e^x+e^x(x^3+7) ?
The first derivative of 3x^2e^x+e^x(x^3+7) is e^xx^3+6e^xx^2+6e^xx+7e^x