What is the derivative of (0.1x/((x+3)^2)) ?

The derivative of (0.1x/((x+3)^2)) is (0.1(3-x))/((x+3)^3)

What is the first derivative of (0.1x/((x+3)^2)) ?

The first derivative of (0.1x/((x+3)^2)) is (0.1(3-x))/((x+3)^3)

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\frac{d}{d x} (\frac{0.1 x}{( x + 3 ) ^{2}})

\frac{0.1 ( 3 - x )}{( x + 3 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{0.1 x}{( x + 3 ) ^{2}})

Take the constant out:

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

= 0.1 \frac{d}{d x} (\frac{x}{( x + 3 ) ^{2}})

Apply the Quotient Rule:

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

= 0.1 \cdot \frac{\frac{d x}{d x} ( x + 3 ) ^{2} - \frac{d}{d x} ( ( x + 3 ) ^{2} ) x}{( ( x + 3 ) ^{2} ) ^{2}}

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

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

= 0.1 \cdot \frac{1 \cdot ( x + 3 ) ^{2} - 2 ( x + 3 ) x}{( ( x + 3 ) ^{2} ) ^{2}}

Simplify

0.1 \cdot \frac{1 \cdot ( x + 3 ) ^{2} - 2 ( x + 3 ) x}{( ( x + 3 ) ^{2} ) ^{2}} : \frac{0.1 ( 3 - x )}{( x + 3 ) ^{3}}

= \frac{0.1 ( 3 - x )}{( x + 3 ) ^{3}}

\frac{d}{d u} (u^{2} - v^{2})

\frac{\partial}{\partial y} (2 x sin (x y))

\int 2 x (3 x - 2)^{6} d x

(5, 9), (4, 5)

x^{\frac{1}{3}}, x = 8

What is the derivative of (0.1x/((x+3)^2)) ?
The derivative of (0.1x/((x+3)^2)) is (0.1(3-x))/((x+3)^3)
What is the first derivative of (0.1x/((x+3)^2)) ?
The first derivative of (0.1x/((x+3)^2)) is (0.1(3-x))/((x+3)^3)