What is the derivative of y=(4ln(3x))/(5+2x) ?

The derivative of y=(4ln(3x))/(5+2x) is (4(5+2x-2xln(3x)))/(x(5+2x)^2)

What is the first derivative of y=(4ln(3x))/(5+2x) ?

The first derivative of y=(4ln(3x))/(5+2x) is (4(5+2x-2xln(3x)))/(x(5+2x)^2)

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derivative of

y = \frac{4 ln ( 3 x )}{5 + 2 x}

\frac{4 ( 5 + 2 x - 2 x ln ( 3 x ) )}{x ( 5 + 2 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 ln ( 3 x )}{5 + 2 x})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{ln ( 3 x )}{5 + 2 x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 4 \cdot \frac{\frac{d}{d x} ( ln ( 3 x ) ) ( 5 + 2 x ) - \frac{d}{d x} ( 5 + 2 x ) ln ( 3 x )}{( 5 + 2 x ) ^{2}}

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

\frac{d}{d x} (5 + 2 x) = 2

= 4 \cdot \frac{\frac{1}{x} ( 5 + 2 x ) - 2 ln ( 3 x )}{( 5 + 2 x ) ^{2}}

Simplify

4 \cdot \frac{\frac{1}{x} ( 5 + 2 x ) - 2 ln ( 3 x )}{( 5 + 2 x ) ^{2}} : \frac{4 ( 5 + 2 x - 2 x ln ( 3 x ) )}{x ( 5 + 2 x ) ^{2}}

= \frac{4 ( 5 + 2 x - 2 x ln ( 3 x ) )}{x ( 5 + 2 x ) ^{2}}

6 cos (t), at t = - \frac{π}{4}

2 s + 1

f (x) = x^{4} - 4 x^{3} + 2 x^{2} - 6, at x = 1

\int \frac{x ^{2}}{x ^{2} + x + 12} d x

\int \frac{1}{- t ^{2} + 3 t - 2} d t

What is the derivative of y=(4ln(3x))/(5+2x) ?
The derivative of y=(4ln(3x))/(5+2x) is (4(5+2x-2xln(3x)))/(x(5+2x)^2)
What is the first derivative of y=(4ln(3x))/(5+2x) ?
The first derivative of y=(4ln(3x))/(5+2x) is (4(5+2x-2xln(3x)))/(x(5+2x)^2)