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Popular Calculus >

derivative of 2^{x^2+x}

Solution

derivative of

2^{x^{2} + x}

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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