What is the derivative of (sin(x+1)/(e^x)) ?

The derivative of (sin(x+1)/(e^x)) is (cos(1+x)-sin(1+x))/(e^x)

What is the first derivative of (sin(x+1)/(e^x)) ?

The first derivative of (sin(x+1)/(e^x)) is (cos(1+x)-sin(1+x))/(e^x)

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\frac{d}{d x} (\frac{sin ( x + 1 )}{e ^{x}})

\frac{cos ( 1 + x ) - sin ( 1 + x )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{sin ( x + 1 )}{e ^{x}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (sin (x + 1)) = cos (x + 1)

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

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

Simplify

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

= \frac{cos ( 1 + x ) - sin ( 1 + x )}{e ^{x}}

\frac{e ^{- 4 x}}{( x - 2 ) ^{2}}

x \to \infty lim ((1 + \frac{c}{x})^{2 x})

\int (10 x^{9} - \frac{9}{x ^{9}}) d x

x \to 1 lim (x^{4} e^{- x^{2}})

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

What is the derivative of (sin(x+1)/(e^x)) ?
The derivative of (sin(x+1)/(e^x)) is (cos(1+x)-sin(1+x))/(e^x)
What is the first derivative of (sin(x+1)/(e^x)) ?
The first derivative of (sin(x+1)/(e^x)) is (cos(1+x)-sin(1+x))/(e^x)