Question

derivative of f (x) = 3 - 4x^2, at x=5

Answer 1

Answer:

$\mathrm{Derivative\:of\:}3-4x^2\mathrm{\:at\:}x=5:\quad -40$

Step-by-step explanation:

$\dfrac{d}{dx}\left(3-4x^2\right)$

$\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'$

$=\dfrac{d}{dx}\left(3\right)-\dfrac{d}{dx}\left(4x^2\right)$

$\dfrac{d}{dx}\left(3\right)$

$\mathrm{Derivative\:of\:a\:constant}:\quad \dfrac{d}{dx}\left(a\right)=0$

$=0$

$\dfrac{d}{dx}\left(4x^2\right)$

$\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'$

$=4\dfrac{d}{dx}\left(x^2\right)$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \dfrac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

$=4\cdot \:2x^{2-1}$

$\mathrm{Simplify}$

$=8x$

$=0-8x$

$\mathrm{Simplify}$

$=-8x$

$\mathrm{Find\:the\:value\:of\:}-8x\mathrm{\:for\:}x=5$

$\mathrm{Plug\:}x=5\mathrm{\:into\:the\:equation\:}-8x$

$-8\cdot \:5$

$\mathrm{Refine}$

$-40$