What is the derivative of log_{3}(4x^2+2x) ?

The derivative of log_{3}(4x^2+2x) is (4x+1)/(ln(3)x(2x+1))

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

The first derivative of log_{3}(4x^2+2x) is (4x+1)/(ln(3)x(2x+1))

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

\frac{4 x + 1}{ln ( 3 ) x ( 2 x + 1 )}

Solution steps

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

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 4 x ^{2} + 2 x )}{ln ( 3 )})

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{2} + 2 x) = 8 x + 2

= \frac{1}{ln ( 3 )} \cdot \frac{1}{4 x ^{2} + 2 x} (8 x + 2)

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{4 x ^{2} + 2 x} (8 x + 2) : \frac{4 x + 1}{ln ( 3 ) x ( 2 x + 1 )}

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

\frac{\partial}{\partial x} (2 x + 3 e^{y} + x y)

\frac{10 s}{( s + 1 ) ( s + 6 )}

\frac{d}{d x} \frac{4 ( y - x \frac{d y}{d x} )}{y ^{2}}

\int \frac{ln ^{2} ( x )}{3 x} d x

\int \frac{6 x + 5}{e ^{x}} d x

What is the derivative of log_{3}(4x^2+2x) ?
The derivative of log_{3}(4x^2+2x) is (4x+1)/(ln(3)x(2x+1))
What is the first derivative of log_{3}(4x^2+2x) ?
The first derivative of log_{3}(4x^2+2x) is (4x+1)/(ln(3)x(2x+1))