Question

Differentiation of 3x³ + 5x² + 7x.........​

Answer 1

Answer

• 9x² + 10x + 7

Given

• 3x³ + 5x² + 7x

To Find

• Differential value

Formula Used

$\boxed{\begin{minipage}{4.5cm} \bullet \;\; \rm \dfrac{d}{dx}(x^n)=n.x^{n-1}\\\\\rm where\ , n\ is\ any\ integer\\\\\bullet \;\; \rm \dfrac{d}{dx}(kx)=k\dfrac{d}{dx}(x)\\\\\rm where\ , k\ is\ constant\ value\end{minipage}}$

Solution

Let , y = 3x³ + 5x² + 7x

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

$\implies \rm \dfrac{d}{dx}(y)=\dfrac{d}{dx}(3x^3+5x^2+7x)\\\\\implies \rm \dfrac{dy}{dx}=\dfrac{d}{dx}(3x^3)+\dfrac{d}{dx}(5x^2)+\dfrac{d}{dx}(7x)\\\\\implies \rm \dfrac{dy}{dx}=3\dfrac{d}{dx}(x^3)+5\dfrac{d}{dx}(x^2)+7\dfrac{d}{dx}(x)\\\\\implies \rm \dfrac{dy}{dx}=3(3.x^{3-1})+5(2.x^{2-1})+7(1.x^{1-1})\\\\\implies \rm \dfrac{dy}{dx}=3(3x^2)+5(2x)+7(x^0)\\\\\implies \bf \dfrac{dy}{dx}=9x^2+10x+7\ [\; Since\ x^0=1\ ]$

Answer 2

Solution :-

Let , y = 3x³ + 5x² + 7x

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

→ $\rm \dfrac{d}{dx}(y)=\dfrac{d}{dx}(3x^3+5x^2+7x)$

→ $\rm \dfrac{dy}{dx}=\dfrac{d}{dx}(3x^3)+\dfrac{d}{dx}(5x^2)+\dfrac{d}{dx}(7x)$

→ $\rm \dfrac{dy}{dx}=3\dfrac{d}{dx}(x^3)+5\dfrac{d}{dx}(x^2)+7\dfrac{d}{dx}(x)$

→ $\rm \dfrac{dy}{dx}=3(3.x^{3-1})+5(2.x^{2-1})+7(1.x^{1-1})$

→ $\rm \dfrac{dy}{dx}=3(3x^2)+5(2x)+7(x^0)$

→ $\bf \dfrac{dy}{dx}=9x^2+10x+7$