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

The derivative of (x^2sin(x)/(e^x)) is (x(xcos(x)+2sin(x)-xsin(x)))/(e^x)

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

The first derivative of (x^2sin(x)/(e^x)) is (x(xcos(x)+2sin(x)-xsin(x)))/(e^x)

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

\frac{x ( x cos ( x ) + 2 sin ( x ) - x sin ( x ) )}{e ^{x}}

Solution steps

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

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

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

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

Simplify

\frac{( 2 x sin ( x ) + cos ( x ) x ^{2} ) e ^{x} - e ^{x} x ^{2} sin ( x )}{( e ^{x} ) ^{2}} : \frac{x ( x cos ( x ) + 2 sin ( x ) - x sin ( x ) )}{e ^{x}}

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

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

- 5 x^{2} y + y^{^{'}} = 5 x^{2}

\int ((sec (x))^{2} - csc (x) cot (x)) d x

x \to 0 lim (\frac{x}{x})

\int sin (x) \cdot sin (3 x) d x

What is the derivative of (x^2sin(x)/(e^x)) ?
The derivative of (x^2sin(x)/(e^x)) is (x(xcos(x)+2sin(x)-xsin(x)))/(e^x)
What is the first derivative of (x^2sin(x)/(e^x)) ?
The first derivative of (x^2sin(x)/(e^x)) is (x(xcos(x)+2sin(x)-xsin(x)))/(e^x)