What is the derivative of (x^2ln(x)/(e^x)) ?

The derivative of (x^2ln(x)/(e^x)) is (x(1+2ln(x)-xln(x)))/(e^x)

What is the first derivative of (x^2ln(x)/(e^x)) ?

The first derivative of (x^2ln(x)/(e^x)) is (x(1+2ln(x)-xln(x)))/(e^x)

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\frac{d}{d x} (\frac{x ^{2} ln ( x )}{e ^{x}})

\frac{x ( 1 + 2 ln ( x ) - x ln ( x ) )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} ln ( x )}{e ^{x}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2} ln (x)) = 2 x ln (x) + x

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

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

Simplify

\frac{( 2 x ln ( x ) + x ) e ^{x} - e ^{x} x ^{2} ln ( x )}{( e ^{x} ) ^{2}} : \frac{x ( 1 + 2 ln ( x ) - x ln ( x ) )}{e ^{x}}

= \frac{x ( 1 + 2 ln ( x ) - x ln ( x ) )}{e ^{x}}

\int_{0}^{4} cos (x) d x

h \to 1 lim (\frac{e ^{h} - 1}{h})

y = - 4 x^{2}, (- 2, - 16)

2 x^{3} + 2 y^{3} - 9 x y = 0, (2, 1)

\int_{0}^{\infty} \frac{ln ( x )}{x} d x

What is the derivative of (x^2ln(x)/(e^x)) ?
The derivative of (x^2ln(x)/(e^x)) is (x(1+2ln(x)-xln(x)))/(e^x)
What is the first derivative of (x^2ln(x)/(e^x)) ?
The first derivative of (x^2ln(x)/(e^x)) is (x(1+2ln(x)-xln(x)))/(e^x)