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

The derivative of (xe^x/(sin(x)+1)) is ((e^x+e^xx)(sin(x)+1)-cos(x)xe^x)/((sin(x)+1)^2)

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

The first derivative of (xe^x/(sin(x)+1)) is ((e^x+e^xx)(sin(x)+1)-cos(x)xe^x)/((sin(x)+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

tan^{2} (3 x)

y = 6 x^{3} ln (5 x)

\frac{x}{2}, 4

\frac{\partial}{\partial x} (yz e^{x z} + 30)

\frac{d}{d x} (cos^{2} (x^{7}))

What is the derivative of (xe^x/(sin(x)+1)) ?
The derivative of (xe^x/(sin(x)+1)) is ((e^x+e^xx)(sin(x)+1)-cos(x)xe^x)/((sin(x)+1)^2)
What is the first derivative of (xe^x/(sin(x)+1)) ?
The first derivative of (xe^x/(sin(x)+1)) is ((e^x+e^xx)(sin(x)+1)-cos(x)xe^x)/((sin(x)+1)^2)