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Popular >

derivative of 5x(1-x/5)^2

Solution

derivative of

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

Solution

5 - 4 x + \frac{3 x ^{2}}{5}

Solution steps

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

Simplify

5 x (1 - \frac{x}{5})^{2} : 5 x - 2 x^{2} + \frac{x ^{3}}{5}

= \frac{d}{d x} (5 x - 2 x^{2} + \frac{x ^{3}}{5})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (5 x) - \frac{d}{d x} (2 x^{2}) + \frac{d}{d x} (\frac{x ^{3}}{5})

\frac{d}{d x} (5 x) = 5

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

\frac{d}{d x} (\frac{x ^{3}}{5}) = \frac{3 x ^{2}}{5}

= 5 - 4 x + \frac{3 x ^{2}}{5}

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Frequently Asked Questions (FAQ)

What is the derivative of 5x(1-x/5)^2 ?
The derivative of 5x(1-x/5)^2 is 5-4x+(3x^2)/5
What is the first derivative of 5x(1-x/5)^2 ?
The first derivative of 5x(1-x/5)^2 is 5-4x+(3x^2)/5