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

The derivative of 5/(sqrt((7-x^2^5))) is (25x)/((7-x^2)^{7/2)}

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

The first derivative of 5/(sqrt((7-x^2^5))) is (25x)/((7-x^2)^{7/2)}

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\frac{d}{d x} \frac{5}{( 7 - x ^{2} ) ^{5}}

\frac{25 x}{( 7 - x ^{2} ) ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} \frac{5}{( 7 - x ^{2} ) ^{5}}

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

5 - \frac{1}{2 ( ( 7 - x ^{2} ) ^{5} ) ^{\frac{3}{2}}} (- 10 x (7 - x^{2})^{4}) : \frac{25 x}{( 7 - x ^{2} ) ^{\frac{7}{2}}}

= \frac{25 x}{( 7 - x ^{2} ) ^{\frac{7}{2}}}

12 x^{5} - 8 x^{4} + 20 x^{3}

\frac{d}{d x} (\frac{sin ( 2 x + 1 )}{cos ( - 1 - 2 x )})

\frac{d ^{2}}{d x ^{2}} (cos (6 x))

x \to - 1 lim (x (0))

x e^{y} y^{^{'}} = 2 (e^{y} + x^{3} e^{2 x})

What is the derivative of 5/(sqrt((7-x^2^5))) ?
The derivative of 5/(sqrt((7-x^2^5))) is (25x)/((7-x^2)^{7/2)}
What is the first derivative of 5/(sqrt((7-x^2^5))) ?
The first derivative of 5/(sqrt((7-x^2^5))) is (25x)/((7-x^2)^{7/2)}