What is the derivative of y=log_{3}(5x^4) ?

The derivative of y=log_{3}(5x^4) is 4/(ln(3)x)

What is the first derivative of y=log_{3}(5x^4) ?

The first derivative of y=log_{3}(5x^4) is 4/(ln(3)x)

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derivative of

y = lo g_{3} (5 x^{4})

\frac{4}{ln ( 3 ) x}

Solution steps

\frac{d}{d x} (lo g_{3} (5 x^{4}))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 5 x ^{4} )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (5 x^{4}))

Apply the chain rule:

\frac{1}{5 x ^{4}} \frac{d}{d x} (5 x^{4})

= \frac{1}{5 x ^{4}} \frac{d}{d x} (5 x^{4})

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

= \frac{1}{ln ( 3 )} \cdot \frac{1}{5 x ^{4}} \cdot 20 x^{3}

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{5 x ^{4}} \cdot 20 x^{3} : \frac{4}{ln ( 3 ) x}

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

2 x^{2} + y^{2} - 7 = 0

\int_{π}^{2 π} - cos (x) d x

x \to 1 lim (\frac{x - x ^{3}}{x - 1})

\frac{d}{d x} (\frac{d ^{2}}{d x ^{2}} (x^{4}) + cos (x) + 1)

\int 3 x^{3} e^{5 x^{4}} d x

What is the derivative of y=log_{3}(5x^4) ?
The derivative of y=log_{3}(5x^4) is 4/(ln(3)x)
What is the first derivative of y=log_{3}(5x^4) ?
The first derivative of y=log_{3}(5x^4) is 4/(ln(3)x)