What is the derivative of 10sqrt(100x-x^2) ?

The derivative of 10sqrt(100x-x^2) is (5(-2x+100))/(sqrt(100x-x^2))

What is the first derivative of 10sqrt(100x-x^2) ?

The first derivative of 10sqrt(100x-x^2) is (5(-2x+100))/(sqrt(100x-x^2))

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\frac{d}{d x} (10 100 x - x^{2})

\frac{5 ( - 2 x + 100 )}{100 x - x ^{2}}

Solution steps

\frac{d}{d x} (10 100 x - x^{2})

Take the constant out:

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

= 10 \frac{d}{d x} (100 x - x^{2})

Apply the chain rule:

\frac{1}{2 100 x - x ^{2}} \frac{d}{d x} (100 x - x^{2})

= \frac{1}{2 100 x - x ^{2}} \frac{d}{d x} (100 x - x^{2})

\frac{d}{d x} (100 x - x^{2}) = 100 - 2 x

= 10 \cdot \frac{1}{2 100 x - x ^{2}} (100 - 2 x)

Simplify

10 \cdot \frac{1}{2 100 x - x ^{2}} (100 - 2 x) : \frac{5 ( - 2 x + 100 )}{100 x - x ^{2}}

= \frac{5 ( - 2 x + 100 )}{100 x - x ^{2}}

e^{k t} (\frac{d y}{d t} + k y) = 0

f (r) = 6 e^{r}

\int 128 tan^{4} (\frac{x}{2}) d x

2 x^{2} y y^{^{'}} + y^{2} = 2

\frac{d}{d x} (- \frac{10}{( 1 + 5 x ) ^{2}})

What is the derivative of 10sqrt(100x-x^2) ?
The derivative of 10sqrt(100x-x^2) is (5(-2x+100))/(sqrt(100x-x^2))
What is the first derivative of 10sqrt(100x-x^2) ?
The first derivative of 10sqrt(100x-x^2) is (5(-2x+100))/(sqrt(100x-x^2))