Question

find the derivative
​

Answer 1

Answer:

$y=lnx^2+sinx\\\\\implies y=2lnx+sinx\\\\\implies \dfrac{dy}{dx}=\boxed{\dfrac{2}{x}+cosx}$

Explanation:

$\dfrac{d}{dx}lnx=\dfrac{1}{x}$

Hence on multiplying both sides by 2 , we get 2/x .

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

Answer 2

Mass of the girl, m = 50 kg

Diameter of the heel, d = 1 cm = 0.01 m

Radius of the heel, r = d/2 = 0.005 m

Area of the heel = πr2

= π (0.005)2

= 7.85 × 10–5 m2

Force exerted by the heel on the floor:

F = mg

= 50 × 9.8

= 490 N

Pressure exerted by the heel on the floor:

P = Force / Area

= 490 / (7.85 × 10-5) = 6.24 × 106 Nm-2

Therefore, the pressure exerted by the heel on the horizontal floor is

6.24 × 106 Nm–2.