What is the derivative of 2xlog_{6}(sqrt(x)) ?

The derivative of 2xlog_{6}(sqrt(x)) is log_{6}(x)+1/(ln(6))

What is the first derivative of 2xlog_{6}(sqrt(x)) ?

The first derivative of 2xlog_{6}(sqrt(x)) is log_{6}(x)+1/(ln(6))

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\frac{d}{d x} (2 x lo g_{6} (x))

lo g_{6} (x) + \frac{1}{ln ( 6 )}

Solution steps

\frac{d}{d x} (2 x lo g_{6} (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x lo g_{6} (x))

Apply the Product Rule:

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

f = x, g = lo g_{6} (x)

= 2 (\frac{d x}{d x} lo g_{6} (x) + \frac{d}{d x} (lo g_{6} (x)) x)

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

\frac{d}{d x} (lo g_{6} (x)) = \frac{1}{2 ln ( 6 ) x}

= 2 (1 \cdot lo g_{6} (x) + \frac{1}{2 ln ( 6 ) x} x)

Simplify

2 (1 \cdot lo g_{6} (x) + \frac{1}{2 ln ( 6 ) x} x) : lo g_{6} (x) + \frac{1}{ln ( 6 )}

= lo g_{6} (x) + \frac{1}{ln ( 6 )}

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What is the derivative of 2xlog_{6}(sqrt(x)) ?
The derivative of 2xlog_{6}(sqrt(x)) is log_{6}(x)+1/(ln(6))
What is the first derivative of 2xlog_{6}(sqrt(x)) ?
The first derivative of 2xlog_{6}(sqrt(x)) is log_{6}(x)+1/(ln(6))