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Popular >

derivative of xye^x

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = y e^{x}

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

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

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

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

Simplify

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

Popular Examples

derivative of (x^2+2x-5/((x+1)^2))

\frac{d}{d x} (\frac{x ^{2} + 2 x - 5}{( x + 1 ) ^{2}})

y^{''}+9/t y^'+(15)/(t^2)y=0

y^{^{''}} + \frac{9}{t} y^{^{'}} + \frac{15}{t ^{2}} y = 0

sum from n=1 to infinity of (3^n)/(2^n)

n = 1 \sum \infty \frac{3 ^{n}}{2 ^{n}}

(\partial)/(\partial x)(2x^{0.5}y^{0.5})

\frac{\partial}{\partial x} (2 x^{0.5} y^{0.5})

derivative of 3x^2+8x-25 derivative of

3 x^{2} + 8 x - 25

Frequently Asked Questions (FAQ)

What is the derivative of xye^x ?
The derivative of xye^x is e^xy+x(e^x(dy)/(dx)+e^xy)
What is the first derivative of xye^x ?
The first derivative of xye^x is e^xy+x(e^x(dy)/(dx)+e^xy)