Let `g: RvecR` be a differentiable function satisfying `g(x)=g(y)g(x-y)AAx , y in R` and `g^(prime)(0)=aa n dg^(prime)(3)=bdot` Then find the value of `g^(prime)(-3)dot`

Let g:R rarr R be a differentiable function satisfying g(x)=g(y)g(x-y)AA x,y in R and g'(0)=a and g'(3)=b. Then find the value of g'(-3)

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of lim_(x->0)(((dy)/(dz)))/x

Let f: RvecR be a function satisfying condition f(x+y^3)=f(x)+[f(y)]^3 for all x ,y in Rdot If f^(prime)(0)geq0, find f(10)dot

Let g(x) be a polynomial function satisfying g(x).g(y) = g(x) + g(y) + g(xy) -2 for all x, y in R and g(1) != 1 . If g(3) = 10 then g(5) equals

Let g(x) be a polynomial function satisfying g(x).g(y) = g(x) + g(y) + g(xy) -2 for all x, y in R and g(1) != 1 . If g(3) = 10 then g(5) equals

Let g\ :[1,6]->[0,\ ) be a real valued differentiable function satisfying g^(prime)(x)=2/(x+g(x)) and g(1)=0, then the maximum value of g cannot exceed

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________