What is the derivative of x^{log_{2}(x}) ?

The derivative of x^{log_{2}(x}) is (2x^{log_{2}(x)-1}ln(x))/(ln(2))

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

The first derivative of x^{log_{2}(x}) is (2x^{log_{2}(x)-1}ln(x))/(ln(2))

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\frac{d}{d x} (x^{l o g_{2} (x)})

\frac{2 x ^{l o g_{2} (x) - 1} ln ( x )}{ln ( 2 )}

Solution steps

\frac{d}{d x} (x^{l o g_{2} (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{l o g_{2} (x)} = e^{l o g_{2} (x) l n (x)}

= \frac{d}{d x} (e^{l o g_{2} (x) l n (x)})

Apply the chain rule:

e^{l o g_{2} (x) l n (x)} \frac{d}{d x} (lo g_{2} (x) ln (x))

= e^{l o g_{2} (x) l n (x)} \frac{d}{d x} (lo g_{2} (x) ln (x))

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

= e^{l o g_{2} (x) l n (x)} \frac{2 ln ( x )}{ln ( 2 ) x}

Simplify

e^{l o g_{2} (x) l n (x)} \frac{2 ln ( x )}{ln ( 2 ) x} : \frac{2 x ^{l o g_{2} (x) - 1} ln ( x )}{ln ( 2 )}

= \frac{2 x ^{l o g_{2} (x) - 1} ln ( x )}{ln ( 2 )}

\int \frac{1}{x ^{2} \cdot x ^{2} - 4} d x

x \to 0 + lim (x^{12} ln (x))

\frac{d}{d x} (ln (x^{2} + 3 x + 3))

f (x) = 4 x^{4} + 3 x^{2} - 1

\frac{d y}{d x} = 4 y x

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