What is the derivative of f(x)=30e^{x^2}x ?

The derivative of f(x)=30e^{x^2}x is 30(2e^{x^2}x^2+e^{x^2})

What is the first derivative of f(x)=30e^{x^2}x ?

The first derivative of f(x)=30e^{x^2}x is 30(2e^{x^2}x^2+e^{x^2})

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derivative of

f (x) = 30 e^{x^{2}} x

30 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{d}{d x} (30 e^{x^{2}} x)

Take the constant out:

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

= 30 \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

= 30 (\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

= 30 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}})

Simplify

30 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}}) : 30 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 30 (2 e^{x^{2}} x^{2} + e^{x^{2}})

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What is the derivative of f(x)=30e^{x^2}x ?
The derivative of f(x)=30e^{x^2}x is 30(2e^{x^2}x^2+e^{x^2})
What is the first derivative of f(x)=30e^{x^2}x ?
The first derivative of f(x)=30e^{x^2}x is 30(2e^{x^2}x^2+e^{x^2})