Question

if

y = x^2+x^2+1

then,

dy/dx = ?????

Answer 1

Given,

y = x² + x² + 1

y = 2x² + 1

Differentiate both sides with respect to x

dy/dx = d(2x² + 1 ) / dx

dy/dx = d(2x²)/dx + d(1)/dx

dy/dx = 2 * 2 * x + 0

dy/dx = 4x .

Therefore, dy/dx = 4x .

We used :

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

d/dx ( k) = 0 , where k is constant.

d/dx ( kx^n ) = k * d/dx ( x^n) , where k is constant.

Answer 2

Hey friend, Harish here.

Here is your answer.

$y = x^2 + x^2 + 1 = 2x^2 +1 \\ \\ Now, By \ using\ sum\ rule\ \\ \\ \frac{d(y)}{dx} = \frac{d}{dx} \bigl( 2x^2 +1 \bigr ) = \frac{d}{dx}(2x^2) + \frac{d}{dx}(1) \\ \\ \to \frac{d}{dx}\bigl( 2x^2\bigr) = (2\times 2x) = 4x \\ \\ \to \frac{d}{dx}(1) = 0 \\ \\ \frac{d}{dx}(2x^2) + \frac{d}{dx}(1) = 4x + 0 = 4x. \\ \\ \boxed{\bold{Therefore \ \frac{d}{dx}(y) = 4x}}$
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Hope my answer is helpful to you.