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Popular >

derivative of x^22^x

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 2^{x}

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

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

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2^{x} = 2^{1 + x}

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

Popular Examples

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\frac{d ^{3}}{d x ^{3}} (\frac{1 - 3 x}{1 + 3 x})

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x \to 0 lim (\frac{sin ( 4 x )}{( 2 x )})

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\int_{2}^{\infty} y e^{- 5 y} d y

area (1/(14x^2)),x,(x/4)area

(\frac{1}{14 x ^{2}}), x, (\frac{x}{4})

derivative of 90x derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of x^22^x ?
The derivative of x^22^x is 2^{1+x}x+ln(2)*2^xx^2
What is the first derivative of x^22^x ?
The first derivative of x^22^x is 2^{1+x}x+ln(2)*2^xx^2