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Popular Calculus >

derivative of (log_{2}(x)^4)

Solution

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

Solution

\frac{4 lo g _{2} ( x ) ^{3}}{ln ( 2 ) x}

Solution steps

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

Apply the chain rule:

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

= 4 (lo g_{2} (x))^{3} \frac{d}{d x} (lo g_{2} (x))

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

= 4 (lo g_{2} (x))^{3} \frac{1}{x ln ( 2 )}

Simplify

4 lo g_{2} (x)^{3} \frac{1}{x ln ( 2 )} : \frac{4 lo g _{2} ( x ) ^{3}}{ln ( 2 ) x}

= \frac{4 lo g _{2} ( x ) ^{3}}{ln ( 2 ) x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (log_{2}(x)^4) ?
The derivative of (log_{2}(x)^4) is (4log_{2}(x)^3)/(ln(2)x)
What is the first derivative of (log_{2}(x)^4) ?
The first derivative of (log_{2}(x)^4) is (4log_{2}(x)^3)/(ln(2)x)