What is the derivative of (2x/(x^2-36)) ?

The derivative of (2x/(x^2-36)) is (2(-x^2-36))/((x^2-36)^2)

What is the first derivative of (2x/(x^2-36)) ?

The first derivative of (2x/(x^2-36)) is (2(-x^2-36))/((x^2-36)^2)

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\frac{d}{d x} (\frac{2 x}{x ^{2} - 36})

\frac{2 ( - x ^{2} - 36 )}{( x ^{2} - 36 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{x ^{2} - 36})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{x ^{2} - 36})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 36 ) - \frac{d}{d x} ( x ^{2} - 36 ) x}{( x ^{2} - 36 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - 36) = 2 x

= 2 \cdot \frac{1 \cdot ( x ^{2} - 36 ) - 2 xx}{( x ^{2} - 36 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x ^{2} - 36 ) - 2 xx}{( x ^{2} - 36 ) ^{2}} : \frac{2 ( - x ^{2} - 36 )}{( x ^{2} - 36 ) ^{2}}

= \frac{2 ( - x ^{2} - 36 )}{( x ^{2} - 36 ) ^{2}}

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 9

x \to - π lim (csc (x))

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{6})

\int \frac{1 - x ^{2}}{( x ^{2} - 1 ) ^{2}} d x

x \to 2 lim (x^{2} - 3 x)

What is the derivative of (2x/(x^2-36)) ?
The derivative of (2x/(x^2-36)) is (2(-x^2-36))/((x^2-36)^2)
What is the first derivative of (2x/(x^2-36)) ?
The first derivative of (2x/(x^2-36)) is (2(-x^2-36))/((x^2-36)^2)