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

The derivative of (2+x^2)(2-x^2)/(2-x) is (3x^4-8x^3+4)/((-x+2)^2)

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

The first derivative of (2+x^2)(2-x^2)/(2-x) is (3x^4-8x^3+4)/((-x+2)^2)

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derivative of

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

\frac{3 x ^{4} - 8 x ^{3} + 4}{( - x + 2 ) ^{2}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 + x^{2}, g = \frac{2 - x ^{2}}{2 - x}

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

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

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

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

Simplify

2 x \frac{2 - x ^{2}}{2 - x} + \frac{x ^{2} - 4 x + 2}{( 2 - x ) ^{2}} (2 + x^{2}) : \frac{3 x ^{4} - 8 x ^{3} + 4}{( - x + 2 ) ^{2}}

= \frac{3 x ^{4} - 8 x ^{3} + 4}{( - x + 2 ) ^{2}}

\int_{0}^{1} \frac{1}{2 x - 1} d x

\frac{\partial}{\partial x} (sec (θ))

\frac{d}{d x} (\frac{( - 2 x ^{3} - 1 )}{( x ^{3} - 1 ) ^{2}})

\int_{0}^{x} 1 + \frac{9}{4} t d t

What is the derivative of (2+x^2)(2-x^2)/(2-x) ?
The derivative of (2+x^2)(2-x^2)/(2-x) is (3x^4-8x^3+4)/((-x+2)^2)
What is the first derivative of (2+x^2)(2-x^2)/(2-x) ?
The first derivative of (2+x^2)(2-x^2)/(2-x) is (3x^4-8x^3+4)/((-x+2)^2)