Question

derivatives of (x^10) in physics​

Answer 1

x¹⁰ = y

f(x) = x¹⁰

f(x + h) = (x + h)¹⁰

• By method of first principle

lim h->0 [ f(x + h) - f(x) ] / h

lim h->0 [ (x + h)¹⁰ - x¹⁰ ] / h

lim h->0 [x¹⁰+¹⁰C1x¹⁰`¹ h+¹⁰C2x¹⁰`² h² +...h¹⁰ - x¹⁰] / h

lim h->0 [¹⁰C1x¹⁰`¹h+¹⁰C2x¹⁰`²h²+¹⁰C3x¹⁰`³h³+...h¹⁰] /h

lim h->0 [h(¹⁰C1¹x⁰`¹+¹⁰C2x¹⁰`²h+¹⁰C3x¹⁰`³h²+..h¹⁰`¹]/h

lim h->0 [10x¹⁰`¹ + ¹⁰C2x¹⁰`²h + ¹⁰C3x¹⁰`³h² +...h¹⁰`¹]

• as lim h->0, his not equal to 0

•°• = (10x¹⁰`¹ + 0 + 0 +...0)

= 10 x¹⁰`¹ = 10x⁹

•°• f(x) = dy/dx = 10x⁹

Answer: Derivatives of x¹⁰ is 10x⁹.