If `f` is defined by `f(x)=x^2-4x+7,` show that `f^(prime)(5)=2f^(prime)(7/2)`

If is a real valued function defined by f(x)=x^2+4x+3, then find f^(prime)(1)a n df^(prime)(3)dot

If f is defined by f(x)=x^2-4x+7 , find f\ '\ (x)

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f is defined by f(x)=x^2, find f^(prime)(2)dot

Let f(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x)a n df^(prime)(0)=0=f^(prime)(x)^2=f(5)dot If n is the minimum number of roots of (f^(prime)(x)^2+f^(prime)(x)f^(x)=0 in the interval [0,6], then the value of n/2 is___

Find the derivative of the function f(x)=2x^2+3x-5 at x = 1 . Also prove that f^(prime)(0)+3f^(prime)(-1)=0 .

If f(x)=|cosx| , find f^(prime)(pi/4) and f^(prime)((3pi)/4) .

Show f:R rarr R defined by f(x)=x^(2)+4x+5 is into