Question

differentiation of y= ax³​

Answer 1

Answer

• dy/dx = 3ax²

Given

• y = ax³

To Find

• dy/dx

Solution

y = ax³

Differentiating with respect to " x " on both sides , we get ,

$\tt \dfrac{d}{dx}(y)=\dfrac{d}{dx}(ax^3)\\\\\implies \tt \dfrac{dy}{dx}=a\dfrac{d}{dx}(x^3)[Since\ a\ is\ constant]\\\\\implies \tt \dfrac{dy}{dx}=a(3x^2)[Since\ \dfrac{d}{dx}(x^n)=n.x^{n-1}]\\\\\implies \tt \dfrac{dy}{dx}=3ax^2$

More Info

$\bullet \tt \;\; \dfrac{d}{dx}(sinx)=cosx\\\\\bullet \tt \;\; \dfrac{d}{dx}(cosx)=-sinx\\\\\bullet \tt \;\; \dfrac{d}{dx}(secx)=secx.tanx\\\\\bullet \tt \;\; \dfrac{d}{dx}(cscx)=-cscx.cotx\\\\ \bullet \tt \;\; \dfrac{d}{dx}(tanx)=sec^2x\\\\\bullet \tt \;\; \dfrac{d}{dx}(cotx)=-csc^2x$