What is the derivative of 2xlog_{4}(sqrt(x)) ?

The derivative of 2xlog_{4}(sqrt(x)) is 2(log_{4}(sqrt(x))+1/(4ln(2)))

What is the first derivative of 2xlog_{4}(sqrt(x)) ?

The first derivative of 2xlog_{4}(sqrt(x)) is 2(log_{4}(sqrt(x))+1/(4ln(2)))

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derivative of

2 x lo g_{4} (x)

2 (lo g_{4} (x) + \frac{1}{4 ln ( 2 )})

Solution steps

\frac{d}{d x} (2 x lo g_{4} (x))

Take the constant out:

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

= 2 \frac{d}{d x} (x lo g_{4} (x))

Apply the Product Rule:

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

f = x, g = lo g_{4} (x)

= 2 (\frac{d x}{d x} lo g_{4} (x) + \frac{d}{d x} (lo g_{4} (x)) x)

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

\frac{d}{d x} (lo g_{4} (x)) = \frac{1}{4 ln ( 2 ) x}

= 2 (1 \cdot lo g_{4} (x) + \frac{1}{4 ln ( 2 ) x} x)

Simplify

2 (1 \cdot lo g_{4} (x) + \frac{1}{4 ln ( 2 ) x} x) : 2 (lo g_{4} (x) + \frac{1}{4 ln ( 2 )})

= 2 (lo g_{4} (x) + \frac{1}{4 ln ( 2 )})

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 z^{3})

\int \frac{2}{3} e^{3 x} x d x

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

\frac{\partial}{\partial y} (x^{4} y - 2 x^{3} y^{2})

x^{5} + 1

What is the derivative of 2xlog_{4}(sqrt(x)) ?
The derivative of 2xlog_{4}(sqrt(x)) is 2(log_{4}(sqrt(x))+1/(4ln(2)))
What is the first derivative of 2xlog_{4}(sqrt(x)) ?
The first derivative of 2xlog_{4}(sqrt(x)) is 2(log_{4}(sqrt(x))+1/(4ln(2)))