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

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

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

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

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

4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

Solution steps

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

Apply the Sum/Difference Rule:

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

= \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)

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

Simplify

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

= 4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

\int_{- 4}^{3} (x^{3} + x^{2} - 6 x) - 6 x d x

y = \frac{1}{x ^{5}}

\int 14 d x

\int 2 π x^{3} sin (x) d x

\frac{\partial}{\partial x} (\frac{y ^{3}}{x ^{2} + y ^{2}})

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