Question

Find dy/dx, if y= 2(x^3)-2x+4. Also find dy/dx,when x=3.​

Answer 1

Explanation:

dy/dx=6x^2_2

substituting 3 we get 6(9)-2=52

Answer 2

Answer:

$\bigstar{\bold{\dfrac{dy}{dx}=6x^{2}-2}}$

$\bigstar{\bold{When\:x=3,\dfrac{dy}{dx}=52}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• y = 2x³ - 2x + 4
• x = 3

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

$\sf{\dfrac{d}{dx} (y)}$

$\sf{\dfrac{d}{dx} (y)\:when\:x=3}$

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Here,

  y = 2x³ - 2x + 4

→ Differentiating with respect to x

  $\sf{\dfrac{dy}{dx}=\dfrac{d}{dx} (2x^{3} -2x+4)}$

→ Differentiating individually

  $\sf{\dfrac{dy}{dx}=\dfrac{d}{dx}(2x^{3})-\dfrac{d}{dx}(2x)+\dfrac{d}{dx}(4)}$

→ Applying identities and taking the constants out,

  $\sf{\dfrac{dy}{dx} =2\times3\times x^{2} -2\times 1 +0}$

  $\sf{\dfrac{dy}{dx}=6x^{2}-2}$

→ Hence the derivative of the function is 6x² - 2

$\boxed{\bold{\dfrac{dy}{dx}=6x^{2}-2}}$

→ Now when x = 3,

  6x² - 2 = 6 × 3² - 2

              = 6 × 9 - 2

              = 54 - 2

              = 52

→ Hence dy/dx when x = 3 is 52

$\boxed{\bold{When\:x=3,\dfrac{dy}{dx}=52}}$

$\Large{\underline{\underline{\bf{Identities\:used:}}}}$

$\sf{\dfrac{d}{dx}(x^{n} )=n\:x^{n-1} }$

$\sf{\dfrac{d}{dx} (k)=0}$

where k = a constant

$\sf{\dfrac{d}{dx}(x)=1}$