What is the derivative of sqrt(10000-40x-0.02x^2) ?

The derivative of sqrt(10000-40x-0.02x^2) is (-0.04x-40)/(2sqrt(10000-40x-0.02x^2))

What is the first derivative of sqrt(10000-40x-0.02x^2) ?

The first derivative of sqrt(10000-40x-0.02x^2) is (-0.04x-40)/(2sqrt(10000-40x-0.02x^2))

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\frac{d}{d x} (10000 - 40 x - 0.02 x^{2})

\frac{- 0.04 x - 40}{2 10000 - 40 x - 0.02 x ^{2}}

Solution steps

\frac{d}{d x} (10000 - 40 x - 0.02 x^{2})

Apply the chain rule:

\frac{1}{2 10000 - 40 x - 0.02 x ^{2}} \frac{d}{d x} (10000 - 40 x - 0.02 x^{2})

= \frac{1}{2 10000 - 40 x - 0.02 x ^{2}} \frac{d}{d x} (10000 - 40 x - 0.02 x^{2})

\frac{d}{d x} (10000 - 40 x - 0.02 x^{2}) = - 0.04 x - 40

= \frac{1}{2 10000 - 40 x - 0.02 x ^{2}} (- 0.04 x - 40)

Simplify

\frac{1}{2 10000 - 40 x - 0.02 x ^{2}} (- 0.04 x - 40) : \frac{- 0.04 x - 40}{2 10000 - 40 x - 0.02 x ^{2}}

= \frac{- 0.04 x - 40}{2 10000 - 40 x - 0.02 x ^{2}}

\int \frac{3 x ^{2} + 14 x + 13}{x + 4} d x

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

\int \frac{x ^{2} - 14 x - 5}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

f (x) = 9 x + 5

y^{^{'}} = t^{2}

What is the derivative of sqrt(10000-40x-0.02x^2) ?
The derivative of sqrt(10000-40x-0.02x^2) is (-0.04x-40)/(2sqrt(10000-40x-0.02x^2))
What is the first derivative of sqrt(10000-40x-0.02x^2) ?
The first derivative of sqrt(10000-40x-0.02x^2) is (-0.04x-40)/(2sqrt(10000-40x-0.02x^2))