Using the first principle, prove that `d/(dx)(1/(f(x)))=(-f^(prime)(x))/([f(x)]^2)`

Using first principles,prove that (d)/(dx)[(1)/(f(x))]=-(f'(x))/((f(x))^(2))

Using first principles,prove that (d)/(dx){(1)/(f(x))}=-(f'(x))/({f(x)}^(2))

Using the first principle,prove that: (d)/(dx)(f(x)g(x))=f(x)(d)/(dx)(g(x))+g(x)(d)/(dx)(f(x))

Differentiate using first principle cos(x^(2)+1)

Let the function ln f(x) is defined where f(x) exists for x>=2 and k is fixed positive real numbers prove that if (d)/(dx)(x.f(x))>=-kf(x) then f(x)>=Ax^(-1-k) where A is independent of x

Prove that (d)/(dx)(cot^(-1)x)=(-1)/((1+x^(2))) , where x in R .

Using mathematical induction prove that : (d)/(dx)(x^(n))=nx^(n-1)f or backslash all n in N

Differentiate the following with respect to x using first principle method. sqrt(x)+(1)/(sqrt(x))

(d)/(dx){(x^(2)-x+1)/(x^(2)+x+1)}=