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Popular >

derivative of 2^xln(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = 2^{x}, g = ln (x)

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

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

Popular Examples

integral of (x^2)/(sqrt(x^3+1))

\int \frac{x ^{2}}{x ^{3} + 1} d x

f (x) = e^{x^{2} + 1}

derivative of f(x)=10^{sqrt(x)}derivative of

f (x) = 1 0^{x}

derivative of (2x/(x^2+4))

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

integral of (x^2-6x+9)/(sqrt(x^2-6x+45))

\int \frac{x ^{2} - 6 x + 9}{x ^{2} - 6 x + 45} d x

Frequently Asked Questions (FAQ)

What is the derivative of 2^xln(x) ?
The derivative of 2^xln(x) is ln(2)*2^xln(x)+(2^x)/x
What is the first derivative of 2^xln(x) ?
The first derivative of 2^xln(x) is ln(2)*2^xln(x)+(2^x)/x