Question

differentiation
(1.) d/dx(x)^n
(2.) d/dx(sinx)
(3.) d/dx(cosx)
(4.) d/dx (ax+b)^n = na(a+b)^n-1​

Answer 1

Answer:

Given: (integral)x^n dx = x^(n+1)/(n+1) + c; Fundamental Theorem of Calculus.

Solve:

(integral)x^(n-1) dx = x^n / n

(d/dx) x^n / n = (d/dx)(integral)x^(n-1) dx = x^(n-1)

1/n (d/dx) x^n = x^(n-1)

(d/dx) x^n = n x^(n-1