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)

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

\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}

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

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

3 x^{\frac{3}{2}}

(2, 3), (7, - 6)

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)