What is the derivative of 4/(2+2x^2) ?

The derivative of 4/(2+2x^2) is -(4x)/((x^2+1)^2)

What is the first derivative of 4/(2+2x^2) ?

The first derivative of 4/(2+2x^2) is -(4x)/((x^2+1)^2)

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derivative of

\frac{4}{2 + 2 x ^{2}}

- \frac{4 x}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{2 + 2 x ^{2}})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{2 + 2 x ^{2}})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((2 + 2 x^{2})^{- 1})

Apply the chain rule:

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

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

\frac{d}{d x} (2 + 2 x^{2}) = 4 x

= 4 (- \frac{1}{( 2 + 2 x ^{2} ) ^{2}} \cdot 4 x)

Simplify

4 (- \frac{1}{( 2 + 2 x ^{2} ) ^{2}} \cdot 4 x) : - \frac{4 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{4 x}{( x ^{2} + 1 ) ^{2}}

\int e^{- (x^{2})} d x

x^{3}, 1

(1 + t^{2}) \frac{d y}{d t} + 4 t y = (1 + t^{2})^{- 2}

x \to \infty + lim (e^{x})

\int_{0}^{3} 0.2 e^{- 0.2 x} d x

What is the derivative of 4/(2+2x^2) ?
The derivative of 4/(2+2x^2) is -(4x)/((x^2+1)^2)
What is the first derivative of 4/(2+2x^2) ?
The first derivative of 4/(2+2x^2) is -(4x)/((x^2+1)^2)