Question

solve it.....,.........​

Answer 1

Given:-

• A function
• y= x³-3x²+3x-2/5

To Find:-

• dy/dx of given function

Solution:-

• On differentiating y w.r.t x, we get

$\longrightarrow\rm{\dfrac{dy}{dx}=x^{3}-3x^{2}+3x-\dfrac{2}{5} }$

$\longrightarrow\rm{\dfrac{dy}{dx}=3x^{2}-3(2x)+3(1)-0}$

$\longrightarrow\rm\green{\dfrac{dy}{dx}=3x^{2}-6x+3}$

━━━━━━━━━━━━━━━━━━━━━━━━━

Formulae to Remember-

$\longrightarrow\rm\green{\dfrac{d(x^{n})}{dx}=nx^{n-1}}$

$\longrightarrow\rm\orange{\dfrac{d(sinx)}{dx}=cosx}$

$\longrightarrow\rm\green{\dfrac{d(cosx)}{dx}=-sinx}$

$\longrightarrow\rm\pink{\dfrac{d(tanx)}{dx}=sec^{2}x}$

$\longrightarrow\rm\green{\dfrac{d(cotx)}{dx}=-cosec^{2}x}$

$\longrightarrow\rm\blue{\dfrac{d(secx)}{dx}=secx.tanx}$

$\longrightarrow\rm\green{\dfrac{d(cosecx)}{dx}=-cosecx.cotx}$

$\longrightarrow\rm\red{\dfrac{d(ln(x))}{dx}=\dfrac{1}{x}}$

$\longrightarrow\rm\green{\dfrac{d(e^{x})}{dx}=e^{x}}$

$\longrightarrow\rm\red{\dfrac{d(f(x))}{dx}=f'(x)}$

$\longrightarrow\rm\green{\dfrac{d(constant)}{dx}=0}$

Answer 2

Step-by-step explanation:

Given:-

• A function
• y= x³-3x²+3x-2/5

To Find:-

dy/dx of given function

Solution:-

On differentiating y w.r.t x, we get

$\longrightarrow\rm{\dfrac{dy}{dx}=x^{3}-3x^{2}+3x-\dfrac{2}{5} }$

$\longrightarrow\rm{\dfrac{dy}{dx}=3x^{2}-3(2x)+3(1)-0}$

$\longrightarrow\rm\green{\dfrac{dy}{dx}=3x^{2}-6x+3}$

━━━━━━━━━━━━━━━━━━━━━━━━━

Formulae to Remember-

$\longrightarrow\rm\green{\dfrac{d(x^{n})}{dx}=nx^{n-1}}$

$\longrightarrow\rm\orange{\dfrac{d(sinx)}{dx}=cosx}$

$\longrightarrow\rm\green{\dfrac{d(cosx)}{dx}=-sinx}$

$\longrightarrow\rm\pink{\dfrac{d(tanx)}{dx}=sec^{2}x}$

$\longrightarrow\rm\green{\dfrac{d(cotx)}{dx}=-cosec^{2}x}$

$\longrightarrow\rm\blue{\dfrac{d(secx)}{dx}=secx.tanx}$

$\longrightarrow\rm\green{\dfrac{d(cosecx)}{dx}=-cosecx.cotx}$

$\longrightarrow\rm\red{\dfrac{d(ln(x))}{dx}=\dfrac{1}{x}}$

$\longrightarrow\rm\green{\dfrac{d(e^{x})}{dx}=e^{x}}$

$\longrightarrow\rm\red{\dfrac{d(f(x))}{dx}=f'(x)}$

$\longrightarrow\rm\green{\dfrac{d(constant)}{dx}=0}$