Let f be a differentiable function satisfying the condition f(xy)=f(x)f(y) for all x,y(≠0)ϵR,f(y)≠0. If f′(1)=2, then f′(x) is equal to
2f(x)
f(x)/x
2xf(x)
2f(x)/x
A
f(x)/x
B
2f(x)/x
C
2f(x)
D
2xf(x)
Open in App
Solution
Verified by Toppr
Was this answer helpful?
8
Similar Questions
Q1
Let f be a differentiable function satisfying the condition f(xy)=f(x)f(y) for all x,y(≠0)ϵR,f(y)≠0. If f′(1)=2, then f′(x) is equal to
View Solution
Q2
If a differentiable function f satisfies f(x+y3)=4−2(f(x)+f(y))3∀x,y∈R, then f(x) is equal to
View Solution
Q3
A function f:R⟶R satisfies the equation f(x+y)=f(x),f(y) for all x,yϵR,f(x)≠0 Suppose that the function is differentiable at x=0 and f′(0)=2 prove that f′(x)=2f(x)
View Solution
Q4
Let f be a function satisfying the condition λf(xy)=f(x)y+f(y)x∀ x, y >0. If f(x) is differentiable and f(1)=1, then the value of limx→∞xf(x) is?
View Solution
Q5
Let f and g be two continuous and differentiable functions satisfying f(x+y)=f(x)+f(y) for all x and y and f(x)=2xg(x)