Given `F(x)=f(x)phi(x)` and `f'(x)phi'(x)=c` then prove that `F''(x)/F(x)=(f'')/f+(phi'')/phi+2c`

If F(x) =f(x) phi (x) and f'(x) phi' (x)=a (a constant), then prove that , (F'')/F=(f'')/f+(phi'')/phi+(2a)/(fphi) , where ''equivd^2/dx^2,'equivd/dx and F(x) ne 0.

Given H(x)=f(x).phi(x) and f prime (x).phi prime(x)=c then prove that (F prime prime prime)/F=(f prime prime prime)/f+(phi prime prime prime)/phi, where c in constant, when f(x),phi(x),F(x) are differentiable

If d/(dx)(phi(x))=f(x) , then

If f(x)=x^(3)-x and phi (x)= sin 2x , then

If f(x)=x^(3)-x and phi (x)= sin 2x , then

Let y=f(x). phi(x) and z=f'(x). phi'(x) prove that (1)/(y)*(d^(2)y)/(dx^(2))=(1)/(f)*(d^(2)f)/(dx^(2))+(1)/(phi)*(d^(2)phi)/(dx^(2))+(2z)/(f phi)

int e^(x){f(x)-f'(x)}dx=phi(x), then int e^(x)f(x)dx is

If y = [f(x)}^(phi(x)) then dy/dx is