Question

differentiate 3x⁴+5 with respect to x.​

Answer 1

Let y = 3x⁴ + 5

Now differentiate y with respect to x

$\implies \bf{\dfrac{d}{dx}(y)=\dfrac{d}{dx}(3x^4+5)}\\\\\implies \bf{\dfrac{dy}{dx}=\dfrac{d}{dx}(3x^4)+\dfrac{d}{dx}(5)}\\\\\implies \bf{\dfrac{dy}{dx}=3\dfrac{d}{dx}(x^4)+5\dfrac{d}{dx}(x^0)}\\\\\implies \bf{\dfrac{dy}{dx}=3(4x^{4-1})+5(0x^{0-1})}\\\\\implies \bf{\dfrac{dy}{dx}=12x^3+0}\\\\\implies \bf{\dfrac{dy}{dx}=12x^3}$

More Info :

$\bullet{\;\;\bf{\dfrac{d}{dx}(k)=0},where\;\;k\ is\ a\ constant.}\\\\\bullet{\;\;\bf{\dfrac{d}{dx}(x^n)=n(x^{n-1})}}\\\\\bullet{\;\;\bf{\dfrac{d}{dx}(kx^{n})=k\dfrac{d}{dx}(x^n)}}}$