What is the derivative of 2^{(x^2+1}) ?

The derivative of 2^{(x^2+1}) is ln(2)*2^{x^2+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+2}x

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

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

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

x \to - 8 lim (2)

\frac{d}{d x} (5 x - 9 x^{2})

\frac{d}{d x} (\frac{x + 4}{x ^{2} + 4})

\int_{- 2 π}^{- π} sin^{2} (x) d x

x \to 3 lim (h (x))

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