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}

t an g e n t f (x) = sin (π - x), at x = \frac{π}{6}

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

\int ln (cos (w)) tan (w) d w

(2 x y) d x + (1 - x^{2}) d y = 0

x \to \infty lim (\frac{ln ( x ) + x ^{3}}{e ^{- x}})

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