What is the derivative of 5/((x^2+2^3)) ?

The derivative of 5/((x^2+2^3)) is -(30x)/((x^2+2)^4)

What is the first derivative of 5/((x^2+2^3)) ?

The first derivative of 5/((x^2+2^3)) is -(30x)/((x^2+2)^4)

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\frac{d}{d x} (\frac{5}{( x ^{2} + 2 ) ^{3}})

- \frac{30 x}{( x ^{2} + 2 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{5}{( x ^{2} + 2 ) ^{3}})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{( x ^{2} + 2 ) ^{3}})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((x^{2} + 2)^{- 3})

Apply the chain rule:

- \frac{3}{( x ^{2} + 2 ) ^{4}} \frac{d}{d x} (x^{2} + 2)

= - \frac{3}{( x ^{2} + 2 ) ^{4}} \frac{d}{d x} (x^{2} + 2)

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

= 5 (- \frac{3}{( x ^{2} + 2 ) ^{4}} \cdot 2 x)

Simplify

5 (- \frac{3}{( x ^{2} + 2 ) ^{4}} \cdot 2 x) : - \frac{30 x}{( x ^{2} + 2 ) ^{4}}

= - \frac{30 x}{( x ^{2} + 2 ) ^{4}}

\int e^{\frac{u}{v}} d u

\int (\frac{u - 2}{u}) d u

\int \frac{X ^{2}}{2} d X

\int 3 x e^{8 x} d x

x \to 0 lim (\frac{3 x ^{2} - 3 x}{x})

What is the derivative of 5/((x^2+2^3)) ?
The derivative of 5/((x^2+2^3)) is -(30x)/((x^2+2)^4)
What is the first derivative of 5/((x^2+2^3)) ?
The first derivative of 5/((x^2+2^3)) is -(30x)/((x^2+2)^4)