What is the derivative of (55)/(0.01x^2+1) ?

The derivative of (55)/(0.01x^2+1) is -(1.1x)/((0.01x^2+1)^2)

What is the first derivative of (55)/(0.01x^2+1) ?

The first derivative of (55)/(0.01x^2+1) is -(1.1x)/((0.01x^2+1)^2)

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derivative of

\frac{55}{0.01 x ^{2} + 1}

- \frac{1.1 x}{( 0.01 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{55}{0.01 x ^{2} + 1})

Take the constant out:

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

= 55 \frac{d}{d x} (\frac{1}{0.01 x ^{2} + 1})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 55 \frac{d}{d x} ((0.01 x^{2} + 1)^{- 1})

Apply the chain rule:

- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (0.01 x^{2} + 1)

= - \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (0.01 x^{2} + 1)

\frac{d}{d x} (0.01 x^{2} + 1) = 0.02 x

= 55 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x)

Simplify

55 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x) : - \frac{1.1 x}{( 0.01 x ^{2} + 1 ) ^{2}}

= - \frac{1.1 x}{( 0.01 x ^{2} + 1 ) ^{2}}

\int tan^{4} (4 t) d t

\frac{\partial}{\partial y} (x y + ln (x + y))

y = 2 x e^{x}, (0, 0)

cos (π x)

\frac{d y}{d x} + y cos (x) = 3 cos (x), y (0) = 5

What is the derivative of (55)/(0.01x^2+1) ?
The derivative of (55)/(0.01x^2+1) is -(1.1x)/((0.01x^2+1)^2)
What is the first derivative of (55)/(0.01x^2+1) ?
The first derivative of (55)/(0.01x^2+1) is -(1.1x)/((0.01x^2+1)^2)