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Popular >

derivative of (log_{2}(x))^2

Solution

derivative of

(lo g_{2} (x))^{2}

Solution

\frac{2 lo g _{2} ( x )}{ln ( 2 ) x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 lo g_{2} (x) \frac{1}{x ln ( 2 )} : \frac{2 lo g _{2} ( x )}{ln ( 2 ) x}

= \frac{2 lo g _{2} ( x )}{ln ( 2 ) x}

Popular Examples

derivative of ((3x^7-7x^2+113)/((5x^3)))

\frac{d}{d x} (\frac{( 3 x ^{7} - 7 x ^{2} + 113 )}{( 5 x ^{3} )})

(\partial)/(\partial x)(x/(y^2+x^2))

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

(dy)/(dx)= 1/x (y^2+0.2y)

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.2 y)

integral of (4x^2+1)/(4x)

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

integral of 3x^2-5x+7/x+2e^3

\int 3 x^{2} - 5 x + \frac{7}{x} + 2 e^{3} d x

Frequently Asked Questions (FAQ)

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