What is the derivative of 7/(sqrt(x^4+3)) ?

The derivative of 7/(sqrt(x^4+3)) is -(14x^3)/((x^4+3)^{3/2)}

What is the first derivative of 7/(sqrt(x^4+3)) ?

The first derivative of 7/(sqrt(x^4+3)) is -(14x^3)/((x^4+3)^{3/2)}

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\frac{d}{d x} (\frac{7}{x ^{4} + 3})

- \frac{14 x ^{3}}{( x ^{4} + 3 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{7}{x ^{4} + 3})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{1}{x ^{4} + 3})

Apply exponent rule:

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

= 7 \frac{d}{d x} ((x^{4} + 3)^{- \frac{1}{2}})

Apply the chain rule:

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

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

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

= 7 (- \frac{1}{2 ( x ^{4} + 3 ) ^{\frac{3}{2}}} \cdot 4 x^{3})

Simplify

7 (- \frac{1}{2 ( x ^{4} + 3 ) ^{\frac{3}{2}}} \cdot 4 x^{3}) : - \frac{14 x ^{3}}{( x ^{4} + 3 ) ^{\frac{3}{2}}}

= - \frac{14 x ^{3}}{( x ^{4} + 3 ) ^{\frac{3}{2}}}

What is the derivative of 7/(sqrt(x^4+3)) ?
The derivative of 7/(sqrt(x^4+3)) is -(14x^3)/((x^4+3)^{3/2)}
What is the first derivative of 7/(sqrt(x^4+3)) ?
The first derivative of 7/(sqrt(x^4+3)) is -(14x^3)/((x^4+3)^{3/2)}