What is the derivative of 38(e^{x^2}+2e^{x^2}x^2) ?

The derivative of 38(e^{x^2}+2e^{x^2}x^2) is 38(4e^{x^2}x^3+6e^{x^2}x)

What is the first derivative of 38(e^{x^2}+2e^{x^2}x^2) ?

The first derivative of 38(e^{x^2}+2e^{x^2}x^2) is 38(4e^{x^2}x^3+6e^{x^2}x)

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derivative of

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

38 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

Solution steps

\frac{d}{d x} (38 (e^{x^{2}} + 2 e^{x^{2}} x^{2}))

Take the constant out:

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

= 38 \frac{d}{d x} (e^{x^{2}} + 2 e^{x^{2}} x^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 38 (\frac{d}{d x} (e^{x^{2}}) + \frac{d}{d x} (2 e^{x^{2}} x^{2}))

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

\frac{d}{d x} (2 e^{x^{2}} x^{2}) = 2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x)

= 38 (e^{x^{2}} \cdot 2 x + 2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x))

Expand

e^{x^{2}} \cdot 2 x + 2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) : 4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

= 38 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

What is the derivative of 38(e^{x^2}+2e^{x^2}x^2) ?
The derivative of 38(e^{x^2}+2e^{x^2}x^2) is 38(4e^{x^2}x^3+6e^{x^2}x)
What is the first derivative of 38(e^{x^2}+2e^{x^2}x^2) ?
The first derivative of 38(e^{x^2}+2e^{x^2}x^2) is 38(4e^{x^2}x^3+6e^{x^2}x)