What is the derivative of 3x^2e^x+e^x(x^3+9) ?

The derivative of 3x^2e^x+e^x(x^3+9) is e^xx^3+6e^xx^2+6e^xx+9e^x

What is the first derivative of 3x^2e^x+e^x(x^3+9) ?

The first derivative of 3x^2e^x+e^x(x^3+9) is e^xx^3+6e^xx^2+6e^xx+9e^x

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derivative of

3 x^{2} e^{x} + e^{x} (x^{3} + 9)

e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 9 e^{x}

Solution steps

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 9))

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} + 9))

\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} + 9)) = e^{x} (x^{3} + 9) + 3 x^{2} e^{x}

= 3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 9) + 3 x^{2} e^{x}

Simplify

3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 9) + 3 x^{2} e^{x} : e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 9 e^{x}

= e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 9 e^{x}

f (x) = \frac{cos ( x )}{x ^{2} - 1}

f (x) = \frac{( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 )}

f (x) = sin (π - x), at x = \frac{π}{6}

\frac{\partial}{\partial y} (x^{2} + y^{2} + 1)

\frac{d}{d x} (\frac{2 x}{x + 1})

What is the derivative of 3x^2e^x+e^x(x^3+9) ?
The derivative of 3x^2e^x+e^x(x^3+9) is e^xx^3+6e^xx^2+6e^xx+9e^x
What is the first derivative of 3x^2e^x+e^x(x^3+9) ?
The first derivative of 3x^2e^x+e^x(x^3+9) is e^xx^3+6e^xx^2+6e^xx+9e^x