What is the derivative of y=x^22^{x^2} ?

The derivative of y=x^22^{x^2} is 2^{1+x^2}x+ln(2)*2^{x^2+1}x^3

What is the first derivative of y=x^22^{x^2} ?

The first derivative of y=x^22^{x^2} is 2^{1+x^2}x+ln(2)*2^{x^2+1}x^3

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derivative of

y = x^{2} 2^{x^{2}}

2^{1 + x^{2}} x + ln (2) \cdot 2^{x^{2} + 1} x^{3}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 2^{x^{2}}

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

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

\frac{d}{d x} (2^{x^{2}}) = ln (2) \cdot 2^{x^{2} + 1} x

= 2 x \cdot 2^{x^{2}} + ln (2) \cdot 2^{x^{2} + 1} x x^{2}

Simplify

2 x \cdot 2^{x^{2}} + ln (2) \cdot 2^{x^{2} + 1} x x^{2} : 2^{1 + x^{2}} x + ln (2) \cdot 2^{x^{2} + 1} x^{3}

= 2^{1 + x^{2}} x + ln (2) \cdot 2^{x^{2} + 1} x^{3}

(x + 3 t) \frac{d x}{d t} + 3 x - t = 0

\frac{d y}{d x} + \frac{7 y}{x} = - 5 x - 10

\frac{\partial}{\partial x} (9 x^{7} y^{6} + 7 x^{5} y^{8})

(3 x - 4)^{2}

f (x) = \frac{5}{1 + x ^{2}}

What is the derivative of y=x^22^{x^2} ?
The derivative of y=x^22^{x^2} is 2^{1+x^2}x+ln(2)*2^{x^2+1}x^3
What is the first derivative of y=x^22^{x^2} ?
The first derivative of y=x^22^{x^2} is 2^{1+x^2}x+ln(2)*2^{x^2+1}x^3