What is the derivative of 2^{x^2-3} ?

The derivative of 2^{x^2-3} is ln(2)*2^{x^2-2}x

What is the first derivative of 2^{x^2-3} ?

The first derivative of 2^{x^2-3} is ln(2)*2^{x^2-2}x

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derivative of

2^{x^{2} - 3}

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

Solution steps

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

Apply exponent rule:

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

2^{x^{2} - 3} = e^{(x^{2} - 3) l n (2)}

= \frac{d}{d x} (e^{(x^{2} - 3) l n (2)})

Apply the chain rule:

e^{(x^{2} - 3) l n (2)} \frac{d}{d x} ((x^{2} - 3) ln (2))

= e^{(x^{2} - 3) l n (2)} \frac{d}{d x} ((x^{2} - 3) ln (2))

\frac{d}{d x} ((x^{2} - 3) ln (2)) = 2 ln (2) x

= e^{(x^{2} - 3) l n (2)} \cdot 2 ln (2) x

Simplify

e^{(x^{2} - 3) l n (2)} \cdot 2 ln (2) x : ln (2) \cdot 2^{x^{2} - 2} x

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

\int_{- \infty}^{20} r e^{\frac{r}{5}} d r

\int \frac{2 x + 1}{x + 1} d x

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

y^{^{'}} = \frac{2 x}{1 + 2 y}, y (0) = 2

\int sec (\frac{x}{5}) d x

What is the derivative of 2^{x^2-3} ?
The derivative of 2^{x^2-3} is ln(2)*2^{x^2-2}x
What is the first derivative of 2^{x^2-3} ?
The first derivative of 2^{x^2-3} is ln(2)*2^{x^2-2}x