What is the derivative of xe^xsin(y) ?

The derivative of xe^xsin(y) is e^xsin(y)+x(e^xsin(y)+e^xcos(y)(dy)/(dx))

What is the first derivative of xe^xsin(y) ?

The first derivative of xe^xsin(y) is e^xsin(y)+x(e^xsin(y)+e^xcos(y)(dy)/(dx))

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x} sin (y)

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x} sin (y) + (e^{x} sin (y) + cos (y) \frac{d y}{d x} e^{x}) x

Simplify

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

y^{^{''}} + 3 y^{^{'}} - 7 y = x^{4} e^{x}

y = x^{2} - 2 x + 2, y = 4

x \to 0 lim (x cot (\frac{1}{4} x))

x^{^{''}} + 2 x^{^{'}} + 5 x = 0

\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}}

What is the derivative of xe^xsin(y) ?
The derivative of xe^xsin(y) is e^xsin(y)+x(e^xsin(y)+e^xcos(y)(dy)/(dx))
What is the first derivative of xe^xsin(y) ?
The first derivative of xe^xsin(y) is e^xsin(y)+x(e^xsin(y)+e^xcos(y)(dy)/(dx))