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Popular >

derivative of 2^{x^2-1}

Solution

\frac{d}{d x} (2^{x^{2} - 1})

Solution

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

Solution steps

\frac{d}{d x} (2^{x^{2} - 1})

Apply exponent rule:

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

2^{x^{2} - 1} = e^{(x^{2} - 1) l n (2)}

= \frac{d}{d x} (e^{(x^{2} - 1) l n (2)})

Apply the chain rule:

e^{(x^{2} - 1) l n (2)} \frac{d}{d x} ((x^{2} - 1) ln (2))

= e^{(x^{2} - 1) l n (2)} \frac{d}{d x} ((x^{2} - 1) ln (2))

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

= e^{(x^{2} - 1) l n (2)} \cdot 2 ln (2) x

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of 2^{x^2-1} ?
The derivative of 2^{x^2-1} is ln(2)*2^{x^2}x
What is the first derivative of 2^{x^2-1} ?
The first derivative of 2^{x^2-1} is ln(2)*2^{x^2}x