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

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

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

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

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derivative of

f (x) = 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}

f (x) = 6 - x, at x = 3

\int x^{2} e^{- 6 x} d x

e x^{2}

\int_{- 2}^{2} (x^{2} - 4) d x

\int \frac{( 2 x + 1 )}{x ^{2} + 4 x + 5} d x

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