What is the derivative of log_{2}((5x-1^3)) ?

The derivative of log_{2}((5x-1^3)) is (15)/(ln(2)(5x-1))

What is the first derivative of log_{2}((5x-1^3)) ?

The first derivative of log_{2}((5x-1^3)) is (15)/(ln(2)(5x-1))

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\frac{d}{d x} (lo g_{2} ((5 x - 1)^{3}))

\frac{15}{ln ( 2 ) ( 5 x - 1 )}

Solution steps

\frac{d}{d x} (lo g_{2} ((5 x - 1)^{3}))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} \frac{ln ( ( 5 x - 1 ) ^{3} )}{ln ( 2 )}

Take the constant out:

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

= \frac{1}{ln ( 2 )} \frac{d}{d x} (ln ((5 x - 1)^{3}))

Apply the chain rule:

\frac{1}{( 5 x - 1 ) ^{3}} \frac{d}{d x} ((5 x - 1)^{3})

= \frac{1}{( 5 x - 1 ) ^{3}} \frac{d}{d x} ((5 x - 1)^{3})

\frac{d}{d x} ((5 x - 1)^{3}) = 15 (5 x - 1)^{2}

= \frac{1}{ln ( 2 )} \cdot \frac{1}{( 5 x - 1 ) ^{3}} \cdot 15 (5 x - 1)^{2}

Simplify

\frac{1}{ln ( 2 )} \cdot \frac{1}{( 5 x - 1 ) ^{3}} \cdot 15 (5 x - 1)^{2} : \frac{15}{ln ( 2 ) ( 5 x - 1 )}

= \frac{15}{ln ( 2 ) ( 5 x - 1 )}

\frac{d}{d x} (\frac{x}{x + \frac{b}{x}})

x \to 3 + lim (a^{2} x - 12 a)

(2 x - 1) d x + (5 y + 4) d y = 0

y = x^{3}, y = 0, x = - 3, x = 3

\frac{1}{( s + 2 ) ^{2} + 9}

What is the derivative of log_{2}((5x-1^3)) ?
The derivative of log_{2}((5x-1^3)) is (15)/(ln(2)(5x-1))
What is the first derivative of log_{2}((5x-1^3)) ?
The first derivative of log_{2}((5x-1^3)) is (15)/(ln(2)(5x-1))