Question

Find the differentiation of 6x³-9x+4

Answer 1

To Find:

Differentiation of 6x³-9x+4

Solution:

We know that,

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

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

Let y= 6x³-9x+4

So, on differentiating y w.r.t. x, we get

$\longrightarrow\mathrm{\dfrac{dy}{dx}=6(3x^{2})-9(1)+0}$

$\longrightarrow\mathrm{\dfrac{dy}{dx}=18x^{2}-9}$

$\longrightarrow\mathrm{\pink{\dfrac{dy}{dx}=9(2x^{2}-1)}}$

Hence, the differentiation of 6x³-9x+4 is 18x²-9 or 9(2x²-1).

More Formulae on differentiation:

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

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

$\longrightarrow\bf{\dfrac{d}{dx}(logx)=\dfrac{1}{x}}$

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

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

$\longrightarrow\bf{\dfrac{d}{dx}(secx)=secxtanx}$

$\longrightarrow\bf{\dfrac{d}{dx}(cosecx)=-cosecxcotx}$

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

$\longrightarrow\bf{\dfrac{d}{dx}(a^{x})=a^{x}loga}$