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

The derivative of 2^xlog_{2}(x) is 2^xln(x)+(2^x)/(ln(2)x)

What is the first derivative of 2^xlog_{2}(x) ?

The first derivative of 2^xlog_{2}(x) is 2^xln(x)+(2^x)/(ln(2)x)

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derivative of

2^{x} lo g_{2} (x)

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

Solution steps

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

Apply the Product Rule:

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

f = 2^{x}, g = lo g_{2} (x)

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

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

\frac{d}{d x} (lo g_{2} (x)) = \frac{1}{x ln ( 2 )}

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

Simplify

2^{x} ln (2) lo g_{2} (x) + \frac{1}{x ln ( 2 )} \cdot 2^{x} : 2^{x} ln (x) + \frac{2 ^{x}}{ln ( 2 ) x}

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

\int \frac{3 x - 1}{x + 1} d x

\frac{\partial}{\partial x} (y - x^{2} - x y^{2})

\int_{1}^{3} 3 x^{2} + \frac{1}{12 x ^{2}} d x

x \to 3 lim (- 4)

13 e^{4 t} \cdot e^{2}

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