Given y= [3]3 x2 + 4, find dydx. Hence find its value at x=0. A student claims that dydx= 13(3x2+4)-

Question

Given y= [3]3 x2 + 4, find dydx. Hence find its value at x=0. A student claims that dydx= 13(3x2+4)-2/3. Explain the error.

Accepted Answer

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{2 x}{\left(3 x^{2} + 4\right)^{\frac{2}{3}}}$; at $x=0$, $0$.

Composite powers