What is the derivative of-(10x/((x^2-9)^2)) ?

The derivative of-(10x/((x^2-9)^2)) is (30(x^2+3))/((x^2-9)^3)

What is the first derivative of-(10x/((x^2-9)^2)) ?

The first derivative of-(10x/((x^2-9)^2)) is (30(x^2+3))/((x^2-9)^3)

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\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 9 ) ^{2}})

\frac{30 ( x ^{2} + 3 )}{( x ^{2} - 9 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 9 ) ^{2}})

Take the constant out:

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

= - 10 \frac{d}{d x} (\frac{x}{( x ^{2} - 9 ) ^{2}})

Apply the Quotient Rule:

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

= - 10 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 9 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 9 ) ^{2} ) x}{( ( x ^{2} - 9 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{2} - 9)^{2}) = 4 x (x^{2} - 9)

= - 10 \cdot \frac{1 \cdot ( x ^{2} - 9 ) ^{2} - 4 x ( x ^{2} - 9 ) x}{( ( x ^{2} - 9 ) ^{2} ) ^{2}}

Simplify

- 10 \cdot \frac{1 \cdot ( x ^{2} - 9 ) ^{2} - 4 x ( x ^{2} - 9 ) x}{( ( x ^{2} - 9 ) ^{2} ) ^{2}} : \frac{30 ( x ^{2} + 3 )}{( x ^{2} - 9 ) ^{3}}

= \frac{30 ( x ^{2} + 3 )}{( x ^{2} - 9 ) ^{3}}

sin (cos (x))

x \to 0 - lim (e^{\frac{9}{x}})

x \to \infty lim (x \cdot 0)

\frac{d y}{d x}, x y + 4 = x

What is the derivative of-(10x/((x^2-9)^2)) ?
The derivative of-(10x/((x^2-9)^2)) is (30(x^2+3))/((x^2-9)^3)
What is the first derivative of-(10x/((x^2-9)^2)) ?
The first derivative of-(10x/((x^2-9)^2)) is (30(x^2+3))/((x^2-9)^3)