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Popular >

derivative of-x^3e^x

Solution

\frac{d}{d x} (- x^{3} e^{x})

Solution

- 3 e^{x} x^{2} - e^{x} x^{3}

Solution steps

\frac{d}{d x} (- x^{3} e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = e^{x}

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

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

\frac{d}{d x} (e^{x}) = e^{x}

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

Simplify

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

= - 3 e^{x} x^{2} - e^{x} x^{3}

Popular Examples

(\partial)/(\partial x)(xe^{(x^2-y)})

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

integral of (x+2)sqrt((3x^2+12x))

\int (x + 2) (3 x^{2} + 12 x) d x

(\partial)/(\partial y)(xy^2+ye^{x^2}+5)

\frac{\partial}{\partial y} (x y^{2} + y e^{x^{2}} + 5)

derivative of y=ln(sqrt(x+5))derivative of

y = ln (x + 5)

limit as x approaches 2 of x^2+6

x \to 2 lim (x^{2} + 6)

Frequently Asked Questions (FAQ)

What is the derivative of-x^3e^x ?
The derivative of-x^3e^x is -3e^xx^2-e^xx^3
What is the first derivative of-x^3e^x ?
The first derivative of-x^3e^x is -3e^xx^2-e^xx^3