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

The derivative of 2x^2sqrt(2-x) is (-5x^2+8x)/(sqrt(2-x))

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

The first derivative of 2x^2sqrt(2-x) is (-5x^2+8x)/(sqrt(2-x))

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

\frac{- 5 x ^{2} + 8 x}{2 - x}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = 2 - x

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

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

\frac{d}{d x} (2 - x) = - \frac{1}{2 2 - x}

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

Simplify

2 (2 x 2 - x + (- \frac{1}{2 2 - x}) x^{2}) : \frac{- 5 x ^{2} + 8 x}{2 - x}

= \frac{- 5 x ^{2} + 8 x}{2 - x}

\frac{d}{d x} (\frac{16}{x ^{2}})

\frac{\partial}{\partial y} (x y^{3} + x^{2})

\int \frac{2 + cos ( x )}{x} d x

\frac{d}{d j} (6 i + 8 j)

\frac{\partial}{\partial y} (8 x sin (y - z))

What is the derivative of 2x^2sqrt(2-x) ?
The derivative of 2x^2sqrt(2-x) is (-5x^2+8x)/(sqrt(2-x))
What is the first derivative of 2x^2sqrt(2-x) ?
The first derivative of 2x^2sqrt(2-x) is (-5x^2+8x)/(sqrt(2-x))