What is the derivative of 2/(sqrt(4+9x^4)) ?

The derivative of 2/(sqrt(4+9x^4)) is -(36x^3)/((4+9x^4)^{3/2)}

What is the first derivative of 2/(sqrt(4+9x^4)) ?

The first derivative of 2/(sqrt(4+9x^4)) is -(36x^3)/((4+9x^4)^{3/2)}

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\frac{d}{d x} (\frac{2}{4 + 9 x ^{4}})

- \frac{36 x ^{3}}{( 4 + 9 x ^{4} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{2}{4 + 9 x ^{4}})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{4 + 9 x ^{4}})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((4 + 9 x^{4})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 4 + 9 x ^{4} ) ^{\frac{3}{2}}} \frac{d}{d x} (4 + 9 x^{4})

= - \frac{1}{2 ( 4 + 9 x ^{4} ) ^{\frac{3}{2}}} \frac{d}{d x} (4 + 9 x^{4})

\frac{d}{d x} (4 + 9 x^{4}) = 36 x^{3}

= 2 (- \frac{1}{2 ( 4 + 9 x ^{4} ) ^{\frac{3}{2}}} \cdot 36 x^{3})

Simplify

2 (- \frac{1}{2 ( 4 + 9 x ^{4} ) ^{\frac{3}{2}}} \cdot 36 x^{3}) : - \frac{36 x ^{3}}{( 4 + 9 x ^{4} ) ^{\frac{3}{2}}}

= - \frac{36 x ^{3}}{( 4 + 9 x ^{4} ) ^{\frac{3}{2}}}

What is the derivative of 2/(sqrt(4+9x^4)) ?
The derivative of 2/(sqrt(4+9x^4)) is -(36x^3)/((4+9x^4)^{3/2)}
What is the first derivative of 2/(sqrt(4+9x^4)) ?
The first derivative of 2/(sqrt(4+9x^4)) is -(36x^3)/((4+9x^4)^{3/2)}