What is the derivative of-(3y)/(3x+2y) ?

The derivative of-(3y)/(3x+2y) is -(9x)/((3x+2y)^2)

What is the first derivative of-(3y)/(3x+2y) ?

The first derivative of-(3y)/(3x+2y) is -(9x)/((3x+2y)^2)

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derivative of

- \frac{3 y}{3 x + 2 y}

- \frac{9 x}{( 3 x + 2 y ) ^{2}}

Solution steps

\frac{d}{d y} (- \frac{3 y}{3 x + 2 y})

Treat

x

as a constant

Take the constant out:

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

= - 3 \frac{d}{d y} (\frac{y}{3 x + 2 y})

Apply the Quotient Rule:

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

= - 3 \cdot \frac{\frac{d y}{d y} ( 3 x + 2 y ) - \frac{d}{d y} ( 3 x + 2 y ) y}{( 3 x + 2 y ) ^{2}}

\frac{d y}{d y} = 1

\frac{d}{d y} (3 x + 2 y) = 2

= - 3 \cdot \frac{1 \cdot ( 3 x + 2 y ) - 2 y}{( 3 x + 2 y ) ^{2}}

Simplify

- 3 \cdot \frac{1 \cdot ( 3 x + 2 y ) - 2 y}{( 3 x + 2 y ) ^{2}} : - \frac{9 x}{( 3 x + 2 y ) ^{2}}

= - \frac{9 x}{( 3 x + 2 y ) ^{2}}

\int 41 tan^{5} (x) sec^{4} (x) d x

x \to 6 lim (\frac{x - 6}{x ^{2} - x})

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 y = 0

10 y^{^{''}} + 1000 y = 140 cos (8 t)

What is the derivative of-(3y)/(3x+2y) ?
The derivative of-(3y)/(3x+2y) is -(9x)/((3x+2y)^2)
What is the first derivative of-(3y)/(3x+2y) ?
The first derivative of-(3y)/(3x+2y) is -(9x)/((3x+2y)^2)