What is the derivative of 3/(sqrt(7x^4-5x^2+1)) ?

The derivative of 3/(sqrt(7x^4-5x^2+1)) is -(3x(14x^2-5))/((7x^4-5x^2+1)^{3/2)}

What is the first derivative of 3/(sqrt(7x^4-5x^2+1)) ?

The first derivative of 3/(sqrt(7x^4-5x^2+1)) is -(3x(14x^2-5))/((7x^4-5x^2+1)^{3/2)}

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\frac{d}{d x} (\frac{3}{7 x ^{4} - 5 x ^{2} + 1})

- \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{3}{7 x ^{4} - 5 x ^{2} + 1})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{7 x ^{4} - 5 x ^{2} + 1})

Apply exponent rule:

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

= 3 \frac{d}{d x} ((7 x^{4} - 5 x^{2} + 1)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{4} - 5 x^{2} + 1)

= - \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{4} - 5 x^{2} + 1)

\frac{d}{d x} (7 x^{4} - 5 x^{2} + 1) = 28 x^{3} - 10 x

= 3 (- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} (28 x^{3} - 10 x))

Simplify

3 (- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} (28 x^{3} - 10 x)) : - \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

= - \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

What is the derivative of 3/(sqrt(7x^4-5x^2+1)) ?
The derivative of 3/(sqrt(7x^4-5x^2+1)) is -(3x(14x^2-5))/((7x^4-5x^2+1)^{3/2)}
What is the first derivative of 3/(sqrt(7x^4-5x^2+1)) ?
The first derivative of 3/(sqrt(7x^4-5x^2+1)) is -(3x(14x^2-5))/((7x^4-5x^2+1)^{3/2)}