What is the derivative of 1/(1+5x^2) ?

The derivative of 1/(1+5x^2) is -(10x)/((1+5x^2)^2)

What is the first derivative of 1/(1+5x^2) ?

The first derivative of 1/(1+5x^2) is -(10x)/((1+5x^2)^2)

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derivative of

\frac{1}{1 + 5 x ^{2}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 5 x + 1, at x = 7

e^{- 3 x}

f (x) = x^{2} cot (x)

\int cos (ln (x)) d x

\int \frac{x ^{2}}{49 + x ^{2}} d x

What is the derivative of 1/(1+5x^2) ?
The derivative of 1/(1+5x^2) is -(10x)/((1+5x^2)^2)
What is the first derivative of 1/(1+5x^2) ?
The first derivative of 1/(1+5x^2) is -(10x)/((1+5x^2)^2)