What is the derivative of xlog_{2}(x-3) ?

The derivative of xlog_{2}(x-3) is (x+ln(x-3)(x-3))/(ln(2)(x-3))

What is the first derivative of xlog_{2}(x-3) ?

The first derivative of xlog_{2}(x-3) is (x+ln(x-3)(x-3))/(ln(2)(x-3))

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\frac{d}{d x} (x lo g_{2} (x - 3))

\frac{x + ln ( x - 3 ) ( x - 3 )}{ln ( 2 ) ( x - 3 )}

Solution steps

\frac{d}{d x} (x lo g_{2} (x - 3))

Apply the Product Rule:

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

f = x, g = lo g_{2} (x - 3)

= \frac{d x}{d x} lo g_{2} (x - 3) + \frac{d}{d x} (lo g_{2} (x - 3)) x

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

\frac{d}{d x} (lo g_{2} (x - 3)) = \frac{1}{ln ( 2 ) ( x - 3 )}

= 1 \cdot lo g_{2} (x - 3) + \frac{1}{ln ( 2 ) ( x - 3 )} x

Simplify

1 \cdot lo g_{2} (x - 3) + \frac{1}{ln ( 2 ) ( x - 3 )} x : \frac{x + ln ( x - 3 ) ( x - 3 )}{ln ( 2 ) ( x - 3 )}

= \frac{x + ln ( x - 3 ) ( x - 3 )}{ln ( 2 ) ( x - 3 )}

(ln (t))^{^{'}}

\frac{3 x - 5}{x ^{2} - 1}

x \to - 2 lim ((x^{3}) (5 - 3 x^{2}))

\frac{d}{d x} (sin (3 x) + cos (6 x))

\int e^{i wt} d t

What is the derivative of xlog_{2}(x-3) ?
The derivative of xlog_{2}(x-3) is (x+ln(x-3)(x-3))/(ln(2)(x-3))
What is the first derivative of xlog_{2}(x-3) ?
The first derivative of xlog_{2}(x-3) is (x+ln(x-3)(x-3))/(ln(2)(x-3))