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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = \frac{1}{0.01 x ^{2} + 1}

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

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

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

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

Simplify

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

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

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