What is the derivative of f(x)=3x^2e^x+e^x(x^3+6) ?

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

What is the first derivative of f(x)=3x^2e^x+e^x(x^3+6) ?

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

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derivative of

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 6)

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

Solution steps

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 6))

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} + 6))

\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} + 6)) = e^{x} (x^{3} + 6) + 3 x^{2} e^{x}

= 3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 6) + 3 x^{2} e^{x}

Simplify

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

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

\frac{d}{d x} (7 sec^{2} (7 x))

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

\int_{0}^{9} x e^{- x^{2}} d x

\frac{1}{x ^{2}}, 1

\frac{\partial}{\partial x} (\frac{x ^{2}}{y} - x z)

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