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

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

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

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

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derivative of

y = 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{\partial}{\partial x} (e^{- 1} cos (π x))

\frac{d x}{d t} = \frac{2 x}{t}, x (3) = 1

10 + t^{2}

\int_{0}^{π} sin^{2} (7 x) d x

\int - sec^{2} (x) d x

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