+0  
 
0
202
1
avatar

Derivative of (x^4)÷(y^8) with respect to x, given dy÷dx=v

Guest Feb 25, 2015

Best Answer 

 #1
avatar+91467 
+5

Derivative of (x^4)÷(y^8) with respect to x, given dy÷dx=v

 

$$\\\frac{d}{dx}\;\frac{x^4}{y^8}\\\\
=\frac{d}{dx}\;x^4*y^{-8}\\\\
=\;4x^3*y^{-8}+x^4*-8y^{-9}\;\;\frac{dy}{dx}\\\\
=\;4x^3*y^{-8}+x^4*-8y^{-9}*v\\\\
=\frac{4x^3}{y^{8}}+\frac{-8x^4v}{y^{9}}\\\\
=\frac{4x^3y-8x^4v}{y^{9}}\\\\
=\frac{4x^3(y-2xv)}{y^{9}}\\\\$$

 

Could a mathematician check  this please ?

Melody  Feb 25, 2015
Sort: 

1+0 Answers

 #1
avatar+91467 
+5
Best Answer

Derivative of (x^4)÷(y^8) with respect to x, given dy÷dx=v

 

$$\\\frac{d}{dx}\;\frac{x^4}{y^8}\\\\
=\frac{d}{dx}\;x^4*y^{-8}\\\\
=\;4x^3*y^{-8}+x^4*-8y^{-9}\;\;\frac{dy}{dx}\\\\
=\;4x^3*y^{-8}+x^4*-8y^{-9}*v\\\\
=\frac{4x^3}{y^{8}}+\frac{-8x^4v}{y^{9}}\\\\
=\frac{4x^3y-8x^4v}{y^{9}}\\\\
=\frac{4x^3(y-2xv)}{y^{9}}\\\\$$

 

Could a mathematician check  this please ?

Melody  Feb 25, 2015

5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details