Question

differentiate the following functions with respect to x.
(i)x^3+5x^2-2
(ii)x sinx
(iii)(2x+3)^6​

Answer 1

Step-by-step explanation:

$\sf (i) y={x}^{3}+5{x}^{2}-2 \\ \\ \sf differenciating\: wr.y \: x \\ \\ \sf \frac{dy}{dx} = 3{x}^{3-1} + 5×2{x}^{2-1} \\ \\ \sf \frac{dy}{dx} = 3{x}^{2} + 10x \\ \\ \sf (ii) y = xsinx \\ \\ \sf \frac{dy}{dx} = \frac{d(x)}{dx}sinx + x \frac{d(sinx)}{dx} \\ \\ \sf \frac{dy}{dx} = sinx + xcosx \\ \\ \sf (iii) y = {(2x+3)}^{6} \\ \\ \sf \frac{dy}{dx} = 6{(2x+3)}^{6-1}\frac{d(2x+3)}{dx} \\ \\ \sf \frac{dy}{dx} = 6×2{(2x+3)}^{5} \\ \\ \sf \frac{dy}{dx} = 12{(2x+3)}^{5}$

NIRANJAN45