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Popular >

derivative of xe^{xy^2}

Solution

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

Solution

e^{x y^{2}} + e^{x y^{2}} x (y^{2} + 2 x y \frac{d y}{d x})

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x y^{2}}

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

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

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

= 1 \cdot e^{x y^{2}} + e^{x y^{2}} (y^{2} + 2 x y \frac{d y}{d x}) x

Simplify

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

Popular Examples

(\partial)/(\partial x)(x/(x^2+y^2+z^2))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2} + z ^{2}})

integral of cos(x)(8+8sin^2(x))

\int cos (x) (8 + 8 sin^{2} (x)) d x

tangent of y=3x^2+2,\at x=1 tangent of

y = 3 x^{2} + 2, at x = 1

integral of xtan(x^2)

\int x tan (x^{2}) d x

(dy)/(dx)=2xy+3y-4x-6

\frac{d y}{d x} = 2 x y + 3 y - 4 x - 6

Frequently Asked Questions (FAQ)

What is the derivative of xe^{xy^2} ?
The derivative of xe^{xy^2} is e^{xy^2}+e^{xy^2}x(y^2+2xy(dy)/(dx))
What is the first derivative of xe^{xy^2} ?
The first derivative of xe^{xy^2} is e^{xy^2}+e^{xy^2}x(y^2+2xy(dy)/(dx))