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

The derivative of (sin(2x))/(e^{x^2)} is (2(cos(2x)-xsin(2x)))/(e^{x^2)}

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

The first derivative of (sin(2x))/(e^{x^2)} is (2(cos(2x)-xsin(2x)))/(e^{x^2)}

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = \frac{y}{x} + 3 x + 5

x \to - 7 lim (- 4 x)

\frac{d}{d x} (\frac{x ^{2} + x - 2}{x ^{2} - 3 x + 4})

\int \frac{2 x + 3}{x ^{2} + 3 x} d x

\int (4 w - 1)^{3} d w

What is the derivative of (sin(2x))/(e^{x^2)} ?
The derivative of (sin(2x))/(e^{x^2)} is (2(cos(2x)-xsin(2x)))/(e^{x^2)}
What is the first derivative of (sin(2x))/(e^{x^2)} ?
The first derivative of (sin(2x))/(e^{x^2)} is (2(cos(2x)-xsin(2x)))/(e^{x^2)}