What is the derivative of 18e^{x^2}x ?

The derivative of 18e^{x^2}x is 18(2e^{x^2}x^2+e^{x^2})

What is the first derivative of 18e^{x^2}x ?

The first derivative of 18e^{x^2}x is 18(2e^{x^2}x^2+e^{x^2})

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derivative of

18 e^{x^{2}} x

18 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{d}{d x} (18 e^{x^{2}} x)

Take the constant out:

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

= 18 \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

= 18 (\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

= 18 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}})

Simplify

18 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}}) : 18 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 18 (2 e^{x^{2}} x^{2} + e^{x^{2}})

\int \frac{e ^{x}}{2 x} d x

y^{^{''}} + 2 y^{^{'}} + 4 y = 5 sin (t)

\int (- x^{2} - 3 x + 6)^{2} d x

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{2 ^{x}}{3 x - 1}

What is the derivative of 18e^{x^2}x ?
The derivative of 18e^{x^2}x is 18(2e^{x^2}x^2+e^{x^2})
What is the first derivative of 18e^{x^2}x ?
The first derivative of 18e^{x^2}x is 18(2e^{x^2}x^2+e^{x^2})