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Popular >

derivative of x^2sqrt(5-x)

Solution

\frac{d}{d x} (x^{2} 5 - x)

Solution

\frac{- 5 x ^{2} + 20 x}{2 5 - x}

Solution steps

\frac{d}{d x} (x^{2} 5 - x)

Apply the Product Rule:

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

f = x^{2}, g = 5 - x

= \frac{d}{d x} (x^{2}) 5 - x + \frac{d}{d x} (5 - x) x^{2}

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

\frac{d}{d x} (5 - x) = - \frac{1}{2 5 - x}

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

Simplify

2 x 5 - x + (- \frac{1}{2 5 - x}) x^{2} : \frac{- 5 x ^{2} + 20 x}{2 5 - x}

= \frac{- 5 x ^{2} + 20 x}{2 5 - x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(5-x) ?
The derivative of x^2sqrt(5-x) is (-5x^2+20x)/(2sqrt(5-x))
What is the first derivative of x^2sqrt(5-x) ?
The first derivative of x^2sqrt(5-x) is (-5x^2+20x)/(2sqrt(5-x))