What is the derivative of 26e^{x^2}x ?

The derivative of 26e^{x^2}x is 26(2e^{x^2}x^2+e^{x^2})

What is the first derivative of 26e^{x^2}x ?

The first derivative of 26e^{x^2}x is 26(2e^{x^2}x^2+e^{x^2})

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\frac{d}{d x} (26 e^{x^{2}} x)

26 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{d}{d x} (26 e^{x^{2}} x)

Take the constant out:

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

= 26 \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

= 26 (\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

= 26 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}})

Simplify

26 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}}) : 26 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 26 (2 e^{x^{2}} x^{2} + e^{x^{2}})

\frac{\partial}{\partial y} (5 x sin (y - z))

\frac{d}{d x} ((7 x^{2} - 12 x) e^{x})

y^{^{'}} - e^{5 x + y} = 0

e^{y} + \frac{( x e ^{y} + 1 ) d y}{d x} = 0

\frac{d}{d x} (\frac{3 x + 2}{5 x - 1})

What is the derivative of 26e^{x^2}x ?
The derivative of 26e^{x^2}x is 26(2e^{x^2}x^2+e^{x^2})
What is the first derivative of 26e^{x^2}x ?
The first derivative of 26e^{x^2}x is 26(2e^{x^2}x^2+e^{x^2})