What is the derivative of (45/(0.01x^2+1)) ?

The derivative of (45/(0.01x^2+1)) is -(0.9x)/((0.01x^2+1)^2)

What is the first derivative of (45/(0.01x^2+1)) ?

The first derivative of (45/(0.01x^2+1)) is -(0.9x)/((0.01x^2+1)^2)

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\frac{d}{d x} (\frac{45}{0.01 x ^{2} + 1})

- \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{45}{0.01 x ^{2} + 1})

Take the constant out:

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

= 45 \frac{d}{d x} (\frac{1}{0.01 x ^{2} + 1})

Apply exponent rule:

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

= 45 \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

= 45 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x)

Simplify

45 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x) : - \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

= - \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

What is the derivative of (45/(0.01x^2+1)) ?
The derivative of (45/(0.01x^2+1)) is -(0.9x)/((0.01x^2+1)^2)
What is the first derivative of (45/(0.01x^2+1)) ?
The first derivative of (45/(0.01x^2+1)) is -(0.9x)/((0.01x^2+1)^2)