What is the derivative of y= 7/(sqrt((1-x^2)^3)) ?

The derivative of y= 7/(sqrt((1-x^2)^3)) is (21x(-x^2+1)^2)/(((1-x^2)^3)^{3/2)}

What is the first derivative of y= 7/(sqrt((1-x^2)^3)) ?

The first derivative of y= 7/(sqrt((1-x^2)^3)) is (21x(-x^2+1)^2)/(((1-x^2)^3)^{3/2)}

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derivative of

y = \frac{7}{( 1 - x ^{2} ) ^{3}}

\frac{21 x ( - x ^{2} + 1 ) ^{2}}{( ( 1 - x ^{2} ) ^{3} ) ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} ((1 - x^{2})^{3}) = - 6 x (1 - x^{2})^{2}

= 7 - \frac{1}{2 ( ( 1 - x ^{2} ) ^{3} ) ^{\frac{3}{2}}} (- 6 x (1 - x^{2})^{2})

Simplify

7 - \frac{1}{2 ( ( 1 - x ^{2} ) ^{3} ) ^{\frac{3}{2}}} (- 6 x (1 - x^{2})^{2}) : \frac{21 x ( - x ^{2} + 1 ) ^{2}}{( ( 1 - x ^{2} ) ^{3} ) ^{\frac{3}{2}}}

= \frac{21 x ( - x ^{2} + 1 ) ^{2}}{( ( 1 - x ^{2} ) ^{3} ) ^{\frac{3}{2}}}

\frac{\partial}{\partial x} (\frac{1}{x ^{4}})

e^{x} (y - 1) d x + 2 (e^{x} + 4) d y = 0

x, 4

\frac{3}{x ^{4} + 7 x + 1}

y^{^{'}} = 3 x y

What is the derivative of y= 7/(sqrt((1-x^2)^3)) ?
The derivative of y= 7/(sqrt((1-x^2)^3)) is (21x(-x^2+1)^2)/(((1-x^2)^3)^{3/2)}
What is the first derivative of y= 7/(sqrt((1-x^2)^3)) ?
The first derivative of y= 7/(sqrt((1-x^2)^3)) is (21x(-x^2+1)^2)/(((1-x^2)^3)^{3/2)}