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Popular >

derivative of x*e^{x^2}

Solution

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

Solution

e^{x^{2}} + 2 e^{x^{2}} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx

Simplify

1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx : e^{x^{2}} + 2 e^{x^{2}} x^{2}

= e^{x^{2}} + 2 e^{x^{2}} x^{2}

Popular Examples

integral of (cot(x))/(sqrt(sin(x)))

\int \frac{cot ( x )}{sin ( x )} d x

derivative of csc(e^{2x})derivative of

csc (e^{2 x})

\frac{1}{p - p ^{2}} d p = d t

area 5x-x^2,x,[0,4]area

5 x - x^{2}, x, [0, 4]

(dy)/(dx)=(e^{2x})/(6y^5)

\frac{d y}{d x} = \frac{e ^{2 x}}{6 y ^{5}}

Frequently Asked Questions (FAQ)

What is the derivative of x*e^{x^2} ?
The derivative of x*e^{x^2} is e^{x^2}+2e^{x^2}x^2
What is the first derivative of x*e^{x^2} ?
The first derivative of x*e^{x^2} is e^{x^2}+2e^{x^2}x^2