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Popular >

derivative of x(1-x/(10))

Solution

\frac{d}{d x} (x (1 - \frac{x}{10}))

Solution

1 - \frac{x}{5}

Solution steps

\frac{d}{d x} (x (1 - \frac{x}{10}))

Apply the Product Rule:

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

f = x, g = 1 - \frac{x}{10}

= \frac{d x}{d x} (1 - \frac{x}{10}) + \frac{d}{d x} (1 - \frac{x}{10}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (1 - \frac{x}{10}) = - \frac{1}{10}

= 1 \cdot (1 - \frac{x}{10}) + (- \frac{1}{10}) x

Simplify

1 \cdot (1 - \frac{x}{10}) + (- \frac{1}{10}) x : 1 - \frac{x}{5}

= 1 - \frac{x}{5}

Graph

Popular Examples

derivative of 5xcos(x^2)

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

limit as x approaches+0 of 5/(x^2+x)-5/x

x \to + 0 lim (\frac{5}{x ^{2} + x} - \frac{5}{x})

derivative of ln((x-1)/(x+1))derivative of

ln (\frac{x - 1}{x + 1})

limit as x approaches 3 of (sin(x))/x

x \to 3 lim (\frac{sin ( x )}{x})

integral of (72)/(1-cos(9x))

\int \frac{72}{1 - cos ( 9 x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of x(1-x/(10)) ?
The derivative of x(1-x/(10)) is 1-x/5
What is the first derivative of x(1-x/(10)) ?
The first derivative of x(1-x/(10)) is 1-x/5