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

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

If f(x) and g(x) are two differentiable functions, show that f(x)g(x) is also differentiable such that (d)/(dx)[f(x)g(x)]=f(x)(d)/(dx){g(x)}+g(x)(d)/(dx){f(x)}

int[(d)/(dx)f(x)]dx=

If (d(f(x))/(dx)=(1)/(1+x^(2)) then (d)/(dx){f(x^(3))} is

Theorem: (d)/(dx)(int f(x)dx=f(x)

If f(x) and g(x) a re differentiate functions, then show that f(x)+-g(x) are also differentiable such that (d)/(dx){f(x)+-g(x)}=(d)/(dx){f(x)}+-(d)/(dx){g(x)}

int_a^b[d/dx(f(x))]dx

If f(x) and g(f) are two differentiable functions and g(x)!=0, then show trht (f(x))/(g(x)) is also differentiable (d)/(dx){(f(x))/(g(x))}=(g(x)(d)/(pi){f(x)}-g(x)(d)/(x){g(x)})/([g(x)]^(2))