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Popular >

derivative of (x^3/(e^x))

Solution

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

Solution

\frac{x ^{2} ( 3 - x )}{e ^{x}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= \frac{3 x ^{2} e ^{x} - e ^{x} x ^{3}}{( e ^{x} ) ^{2}}

Simplify

\frac{3 x ^{2} e ^{x} - e ^{x} x ^{3}}{( e ^{x} ) ^{2}} : \frac{x ^{2} ( 3 - x )}{e ^{x}}

= \frac{x ^{2} ( 3 - x )}{e ^{x}}

Graph

Popular Examples

(\partial)/(\partial x)(-3ycos(-9x))

\frac{\partial}{\partial x} (- 3 y cos (- 9 x))

derivative of f(x)= 1/(r+3e^r)derivative of

f (x) = \frac{1}{r + 3 e ^{r}}

(8 + x) y^{^{'}} = 9 y

(\partial)/(\partial x)(y^2+2xy+7y+7x)

\frac{\partial}{\partial x} (y^{2} + 2 x y + 7 y + 7 x)

limit as x approaches pi of c*cos(x)

x \to π lim (c \cdot cos (x))

Frequently Asked Questions (FAQ)

What is the derivative of (x^3/(e^x)) ?
The derivative of (x^3/(e^x)) is (x^2(3-x))/(e^x)
What is the first derivative of (x^3/(e^x)) ?
The first derivative of (x^3/(e^x)) is (x^2(3-x))/(e^x)