Question

Differentiate f(x)=x^3+2x^2+5x+100

Answer 1

$\bf We\:\: Have$

$\rm\to \dfrac{d(x^3+2x^2+5x+100)}{dx}$

$\bf For\:Differentiation\:we\:use\:this\;Rule$

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

$\bf We\:\: Write \:\: as$

$\rm\to \dfrac{d(x^3)}{dx} +2\dfrac{d(x^2)}{dx} +5\dfrac{d(x)}{dx} +\dfrac{d(100)}{dx}$

$\rm\to 3x^{3-1} + 2\times2x^{2-1}+5 \times 1 + 0$

$\rm\to 3x^2+4x+5$

$\bf Answer$

$\rm\to 3x^2+4x+5$

$\bf MORE\:\: INFORMATION$

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

$\rm\to\dfrac{d}{dx}(ax)=a$

$\rm\to\dfrac{d}{dx}(Cosx)=-Sinx$

$\rm\to\dfrac{d}{dx}(Sinx)=Cosx$

$\rm\to\dfrac{d}{dx}(tanx)=Sec^2x$

$\rm\to\dfrac{d}{dx}(secx)=Secxtanx$

$\rm\to\dfrac{d}{dx}(lnx)= \dfrac{1}{x}$