What is the derivative of (160(x+1))/((x+2)^2) ?

The derivative of (160(x+1))/((x+2)^2) is -(160x)/((x+2)^3)

What is the first derivative of (160(x+1))/((x+2)^2) ?

The first derivative of (160(x+1))/((x+2)^2) is -(160x)/((x+2)^3)

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derivative of

\frac{160 ( x + 1 )}{( x + 2 ) ^{2}}

- \frac{160 x}{( x + 2 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{160 ( x + 1 )}{( x + 2 ) ^{2}})

Take the constant out:

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

= 160 \frac{d}{d x} (\frac{x + 1}{( x + 2 ) ^{2}})

Apply the Quotient Rule:

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

= 160 \cdot \frac{\frac{d}{d x} ( x + 1 ) ( x + 2 ) ^{2} - \frac{d}{d x} ( ( x + 2 ) ^{2} ) ( x + 1 )}{( ( x + 2 ) ^{2} ) ^{2}}

\frac{d}{d x} (x + 1) = 1

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

= 160 \cdot \frac{1 \cdot ( x + 2 ) ^{2} - 2 ( x + 2 ) ( x + 1 )}{( ( x + 2 ) ^{2} ) ^{2}}

Simplify

160 \cdot \frac{1 \cdot ( x + 2 ) ^{2} - 2 ( x + 2 ) ( x + 1 )}{( ( x + 2 ) ^{2} ) ^{2}} : - \frac{160 x}{( x + 2 ) ^{3}}

= - \frac{160 x}{( x + 2 ) ^{3}}

y^{^{''}} - 16 y = 0

\int \frac{2 x ^{2}}{2 x ^{2} + 1} d x

\int x (2 x^{2} - 1)^{4} d x

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

\frac{d}{d t} (t^{2} e^{- t})

What is the derivative of (160(x+1))/((x+2)^2) ?
The derivative of (160(x+1))/((x+2)^2) is -(160x)/((x+2)^3)
What is the first derivative of (160(x+1))/((x+2)^2) ?
The first derivative of (160(x+1))/((x+2)^2) is -(160x)/((x+2)^3)