Question

find d/dx of the function
f(x) = x^2/3 ​

Answer 1

$\bf \large f(x) = \dfrac{ {x}^{2} }{3}$

Differentiating both sides :

$\implies\sf \dfrac{d(f(x))}{dx} = \dfrac{d(\dfrac{ {x}^{2} }{3})}{dx}$

$\implies\sf \dfrac{d(f(x))}{dx} = \dfrac{1}{3} \dfrac{d{ ({x}^{2}) }}{dx}$

We know that :-

$\underline{ \boxed{\bf \large \dfrac{d{ ({x}^{n}) }}{dx} = a \: {x}^{n - 1} }}$

$\sf \implies \dfrac{d(f(x))}{dx} = \dfrac{1}{3} \times 2 \times ({x})^{2 - 1}$

$\sf \implies \dfrac{d(f(x))}{dx} = \dfrac{2x}{3}$

Answer :

• d/dx of the function f(x) = x^2/3 = 2x/3

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$\pink{\underline {\large\bf\blue{Additional-Information}}}$

d(sinx)/dx = cosx

d(cos x)/dx = -sin x

d(cosec x)/dx = -cot x cosec x

d(tan x)/dx = sec²x

d(sec x)/dx = secx tanx

d(cot x)/dx = - cosec² x

d(x^n)/dx = n x^(n-1)

d(log x)/dx = 1/x

d(e^x)/dx = e^x