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Derivative of $x^2$ w.r.t $x^3$ is _____________.

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Toolbox:
  • If the variable $x$ and $y$ are connected by a relation of the form $f(x,y)=0$ and it is not possible to express $y$ as a function of $x$,then it is said to be implicit function.
  • Hence $\phi(y)$ w.r.t $x$ is $\large\frac{d\phi}{dy}.\frac{dy}{dx}$
Let $u=x^2$
$v=x^3$
$\large\frac{du}{dx}$$=2x$
$\large\frac{dv}{dx}$$=3x^2$
Therefore $\large\frac{\Large\frac{du}{dx}}{\Large\frac{dv}{dx}}=\large\frac{2x}{3x^2}=\large\frac{2}{3x}$
Derivative of $x^2$ w.r.t $x^3$ is $\large\frac{2}{3x}$
answered Jul 4, 2013 by sreemathi.v
 
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