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Popular >

derivative of xlog_{2}(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

sum from n=1 to infinity of-1/(8^n)

n = 1 \sum \infty - \frac{1}{8 ^{n}}

integral of (4x^2-x+5)/(12x)

\int \frac{4 x ^{2} - x + 5}{12 x} d x

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\int \frac{x ^{5}}{x ^{2} + 3} d x

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\int_{0}^{4} (2 t + 4) d t

derivative of 10(4e^{x^2}x^3+6e^{x^2}x)derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of xlog_{2}(x) ?
The derivative of xlog_{2}(x) is log_{2}(x)+1/(ln(2))
What is the first derivative of xlog_{2}(x) ?
The first derivative of xlog_{2}(x) is log_{2}(x)+1/(ln(2))