What is the derivative of 22e^{x^2}x ?

The derivative of 22e^{x^2}x is 22(2e^{x^2}x^2+e^{x^2})

What is the first derivative of 22e^{x^2}x ?

The first derivative of 22e^{x^2}x is 22(2e^{x^2}x^2+e^{x^2})

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derivative of

22 e^{x^{2}} x

22 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{d}{d x} (22 e^{x^{2}} x)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 22 \frac{d}{d x} (e^{x^{2}} x)

Apply the Product Rule:

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

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

= 22 (\frac{d}{d x} (e^{x^{2}}) x + \frac{d x}{d x} e^{x^{2}})

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

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

= 22 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}})

Simplify

22 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}}) : 22 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 22 (2 e^{x^{2}} x^{2} + e^{x^{2}})

n = 0 \sum \infty \frac{( 9 ^{n} )}{n !}

\int \frac{x + 3}{x ^{2} + 2 x + 2} d x

\int_{0}^{2} e^{x} d x

x^{2} + 1, x + 3, 0

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

What is the derivative of 22e^{x^2}x ?
The derivative of 22e^{x^2}x is 22(2e^{x^2}x^2+e^{x^2})
What is the first derivative of 22e^{x^2}x ?
The first derivative of 22e^{x^2}x is 22(2e^{x^2}x^2+e^{x^2})