What is the derivative of 8/(sqrt((9x^2-7^5))) ?

The derivative of 8/(sqrt((9x^2-7^5))) is -(360x)/((9x^2-7)^{7/2)}

What is the first derivative of 8/(sqrt((9x^2-7^5))) ?

The first derivative of 8/(sqrt((9x^2-7^5))) is -(360x)/((9x^2-7)^{7/2)}

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\frac{d}{d x} \frac{8}{( 9 x ^{2} - 7 ) ^{5}}

- \frac{360 x}{( 9 x ^{2} - 7 ) ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} \frac{8}{( 9 x ^{2} - 7 ) ^{5}}

Take the constant out:

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

= 8 \frac{d}{d x} \frac{1}{( 9 x ^{2} - 7 ) ^{5}}

Apply exponent rule:

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

= 8 \frac{d}{d x} (((9 x^{2} - 7)^{5})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( ( 9 x ^{2} - 7 ) ^{5} ) ^{\frac{3}{2}}} \frac{d}{d x} ((9 x^{2} - 7)^{5})

= - \frac{1}{2 ( ( 9 x ^{2} - 7 ) ^{5} ) ^{\frac{3}{2}}} \frac{d}{d x} ((9 x^{2} - 7)^{5})

\frac{d}{d x} ((9 x^{2} - 7)^{5}) = 90 x (9 x^{2} - 7)^{4}

= 8 - \frac{1}{2 ( ( 9 x ^{2} - 7 ) ^{5} ) ^{\frac{3}{2}}} \cdot 90 x (9 x^{2} - 7)^{4}

Simplify

8 - \frac{1}{2 ( ( 9 x ^{2} - 7 ) ^{5} ) ^{\frac{3}{2}}} \cdot 90 x (9 x^{2} - 7)^{4} : - \frac{360 x}{( 9 x ^{2} - 7 ) ^{\frac{7}{2}}}

= - \frac{360 x}{( 9 x ^{2} - 7 ) ^{\frac{7}{2}}}

What is the derivative of 8/(sqrt((9x^2-7^5))) ?
The derivative of 8/(sqrt((9x^2-7^5))) is -(360x)/((9x^2-7)^{7/2)}
What is the first derivative of 8/(sqrt((9x^2-7^5))) ?
The first derivative of 8/(sqrt((9x^2-7^5))) is -(360x)/((9x^2-7)^{7/2)}