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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derivative of

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

\frac{9}{x + 2}

\frac{\partial}{\partial x} (x y e^{z} + x - z^{2} - 3)

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

\int sin^{3} (10 x) d x

y = x^{2} - x + 4, at x = 4

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