What is the derivative of 10e^{x^2}x ?

The derivative of 10e^{x^2}x is 10(2e^{x^2}x^2+e^{x^2})

What is the first derivative of 10e^{x^2}x ?

The first derivative of 10e^{x^2}x is 10(2e^{x^2}x^2+e^{x^2})

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derivative of

10 e^{x^{2}} x

10 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{d}{d x} (10 e^{x^{2}} x)

Take the constant out:

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

= 10 \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

= 10 (\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

= 10 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}})

Simplify

10 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}}) : 10 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 10 (2 e^{x^{2}} x^{2} + e^{x^{2}})

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

\int \frac{1}{sin ^{2} ( x ) + 1} d x

\frac{\partial}{\partial x} (2 1 - y^{2})

(14 + x) \frac{d y}{d x} = 5 y

\frac{d y}{d x} = \frac{( x - 1 )}{y - 1}

What is the derivative of 10e^{x^2}x ?
The derivative of 10e^{x^2}x is 10(2e^{x^2}x^2+e^{x^2})
What is the first derivative of 10e^{x^2}x ?
The first derivative of 10e^{x^2}x is 10(2e^{x^2}x^2+e^{x^2})