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

The derivative of 2^x+x^2e^{x^2} is 2^xln(2)+2e^{x^2}x+2e^{x^2}x^3

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

The first derivative of 2^x+x^2e^{x^2} is 2^xln(2)+2e^{x^2}x+2e^{x^2}x^3

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derivative of

2^{x} + x^{2} e^{x^{2}}

2^{x} ln (2) + 2 e^{x^{2}} x + 2 e^{x^{2}} x^{3}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

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

= 2^{x} ln (2) + 2 e^{x^{2}} x + 2 e^{x^{2}} x^{3}

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