What is (\partial)/(\partial x)(2^{x^2}) ?

The answer to (\partial)/(\partial x)(2^{x^2}) is ln(2)*2^{x^2+1}x

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(\partial)/(\partial x)(2^{x^2})

\frac{\partial}{\partial x} (2^{x^{2}})

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

Solution steps

\frac{\partial}{\partial x} (2^{x^{2}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{x^{2}} = e^{x^{2} l n (2)}

= \frac{\partial}{\partial x} (e^{x^{2} l n (2)})

Apply the chain rule:

e^{x^{2} l n (2)} \frac{\partial}{\partial x} (x^{2} ln (2))

= e^{x^{2} l n (2)} \frac{\partial}{\partial x} (x^{2} ln (2))

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

= e^{x^{2} l n (2)} \cdot 2 ln (2) x

Simplify

e^{x^{2} l n (2)} \cdot 2 ln (2) x : ln (2) \cdot 2^{x^{2} + 1} x

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

\frac{d}{d θ} (1 + cos (2 θ))

x^{2}, 6 - x, [- 3, 2]

\frac{d}{d x} (- 2 e^{3 x} sin (2 x))

f (x) = \frac{4 x}{( x ^{3} - 6 ) ^{2}}

What is (\partial)/(\partial x)(2^{x^2}) ?
The answer to (\partial)/(\partial x)(2^{x^2}) is ln(2)*2^{x^2+1}x