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

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

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

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

If (d)/(dx)[g(x)]=f(x) , then : int_(a)^(b)f(x)g(x)dx=

if (d)/(dx)f(x)=g(x), find the value of int_(a)^(b)f(x)g(x)dx

If (d)/(dx)[f(x)]=(1)/(1+x^(2))," then: "(d)/(dx)[f(x^(3))]=

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)}

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

Let f(x) be a differentiable and let c a be a constant.Then cf(x) is also differentiable such that (d)/(dx){cf(x)}=c(d)/(dx)(f(x))

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)}