Question

f(x)= 4-x
$4 -x {}^{2}$
find the derivative

Answer 1

Find the Derivative f(x)=4+x^2

f(x)=4+x2f(x)=4+x2

By the Sum Rule, the derivative of 4+x24+x2 with respect to xx is ddx[4]+ddx[x2]ddx[4]+ddx[x2].

ddx[4]+ddx[x2]ddx[4]+ddx[x2]

Since 44 is constant with respect to xx, the derivative of 44 with respect to xx is 00.

0+ddx[x2]0+ddx[x2]

Differentiate using the Power Rule which states that ddx[xn]ddx[xn] is nxn−1nxn-1 where n=2n=2.

0+2x0+2x

Add 00 and 2x2x to get 2x2x.

2x

just change the sign of + to -