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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 36 \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}}

= 36 \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

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

Simplify

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

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

f (x) = (4 + 5 x)^{2}, (- 3, 121)

f (x) = 2 x, (18, 6)

\frac{d y}{d x} = \frac{e ^{y} + 1}{e ^{y}}

x = - 2, x = 1, y = 2 x^{2} + 7, y = 0

y^{^{'}} + 2 x y = 2 x e^{- x^{2}}

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