What is the derivative of y=log_{4}(x)+log_{4}(x^2) ?

The derivative of y=log_{4}(x)+log_{4}(x^2) is 3/(2ln(2)x)

What is the first derivative of y=log_{4}(x)+log_{4}(x^2) ?

The first derivative of y=log_{4}(x)+log_{4}(x^2) is 3/(2ln(2)x)

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derivative of

y = lo g_{4} (x) + lo g_{4} (x^{2})

\frac{3}{2 ln ( 2 ) x}

Solution steps

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

Simplify

lo g_{4} (x) + lo g_{4} (x^{2}) : lo g_{4} (x^{3})

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

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x ^{3} )}{ln ( 4 )})

Take the constant out:

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

= \frac{1}{ln ( 4 )} \frac{d}{d x} (ln (x^{3}))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{ln ( 4 )} \cdot \frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{3}{2 ln ( 2 ) x}

= \frac{3}{2 ln ( 2 ) x}

\frac{d}{d x} (x^{2} - 8)

(0, 2), (2, - 3)

δ (x)

x^{2} e^{x - 1} 1

e^{- 2 t}

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